5411 + Interview Questions in Quantitative Aptitude Page 102 InterviewSolution

5051.	A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminum of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square. Find the area of the part of the circle (round punch) falling outside the square sheet.
Answer» A punching machine is used to punch a circular hole of diameter two units from a square sheet of aluminum of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square. Find the area of the part of the circle (round punch) falling outside the square sheet.

Discussion

5052.	Q38. In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain?
Answer» Q38. In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain?

Discussion

5053.	Ajay and his wife Kajol appear in an interview for two vacancies in the same post. The probability of Ajay's selection is 17 and that of his wife Kajol's selection is 15. What is the probability that only one of them will be selected?
Answer» Ajay and his wife Kajol appear in an interview for two vacancies in the same post. The probability of Ajay's selection is $\frac{1}{7}$ and that of his wife Kajol's selection is $\frac{1}{5}$ . What is the probability that only one of them will be selected?

Discussion

5054.	The average weight of a b and c is 45kg. if the average weight of A and B be 40kg and that of B and C be 43kg then find the weight of B
Answer» The average weight of a b and c is 45kg. if the average weight of A and B be 40kg and that of B and C be 43kg then find the weight of B

Discussion

5055.	Anita, Sunita, Ram and Raman scored 89, 87, 90 and 55 marks (out of 100) respectively in an exam. Who scored the maximum percentage and how much is that value?
Answer» Anita, Sunita, Ram and Raman scored 89, 87, 90 and 55 marks (out of 100) respectively in an exam. Who scored the maximum percentage and how much is that value?

Discussion

5056.	x2+px+q=0 in the equation there r α and β, show 1α+β and (1α+1β) in which equation is pqx2+(p2+q)x+p=0
Answer» $x^{2} + p x + q = 0$ in the equation there r $α a n d β$ , show $\frac{1}{α + β} a n d (\frac{1}{α} + \frac{1}{β})$ in which equation is $p q x^{2} + (p^{2} + q) x + p = 0$

Discussion

5057.	A toy is in the shape of a hemisphere surmounted by a cone. If the radius of the base of the cone is 3cm and height is 4cm, the total surface area of the toy is :
Answer» A toy is in the shape of a hemisphere surmounted by a cone. If the radius of the base of the cone is 3cm and height is 4cm, the total surface area of the toy is :

Discussion

5058.	Companies that offer ''employer sponsored insurance'' (ESI) pay a portion of employees’ health care costs. In the manufacturing sector last year, companies that offered ESI had worker absentee rates 22%lower, on average, than those at companies that did not offer ESI. If, on the basis of the evidence above, it is argued that ESI decreases worker absenteeism, which of the following, if true, would most seriously weaken that argument?
Answer» Companies that offer ''employer sponsored insurance'' (ESI) pay a portion of employees’ health care costs. In the manufacturing sector last year, companies that offered ESI had worker absentee rates $22 %$ lower, on average, than those at companies that did not offer ESI. If, on the basis of the evidence above, it is argued that ESI decreases worker absenteeism, which of the following, if true, would most seriously weaken that argument?

Discussion

5059.	A student took fine papers in an examination where the full marks were the same for each paper. His marks in these papers were 6:7:8:9. He obtained (35) part of the total full marks. Then the numbers of papers in which he got more than 50 marks is ___
Answer» A student took fine papers in an examination where the full marks were the same for each paper. His marks in these papers were 6:7:8:9. He obtained $(\frac{3}{5})$ part of the total full marks. Then the numbers of papers in which he got more than 50 marks is ___

Discussion

5060.	What is the volume of 2g O2 at 0 degree centigrade and 760 mm pressure of Hg?
Answer» What is the volume of 2g $O_{2}$ at 0 degree centigrade and 760 mm pressure of Hg?

Discussion

5061.	Find the 300th term in the series A26, B25, B25, C24, C24, C24 , D23, ……
Answer» Find the 300^th term in the series A26, B25, B25, C24, C24, C24 , D23, $\dots \dots$

Discussion

5062.	On 1st August, 2016, a survey was conducted in a restaurant regarding flow of customer, type of customer, collection of money at the counter. The results are compiled in the table below. Only one bill is issued per single customer or per customer group. Group here means more than one customer at one time. This represents a typical day’s scenario and all working days of the month will show the same data on each day. During which 2-hour interval during the day is the collection amount maximum?
Answer» On 1st August, 2016, a survey was conducted in a restaurant regarding flow of customer, type of customer, collection of money at the counter. The results are compiled in the table below. Only one bill is issued per single customer or per customer group. Group here means more than one customer at one time. This represents a typical day’s scenario and all working days of the month will show the same data on each day. During which 2-hour interval during the day is the collection amount maximum?

Discussion

5063.	If a,b,c are the lengths of the perpendiculars dropped from a point inside on an equilateral triangle of side "p” on its sides, then find a+b+c
Answer» If a,b,c are the lengths of the perpendiculars dropped from a point inside on an equilateral triangle of side "p” on its sides, then find a+b+c

Discussion

5064.	Let two adjacent sides of a parallelogram be a and b while the diagonals be x and y. Then x2+y2 is ___
Answer» Let two adjacent sides of a parallelogram be a and b while the diagonals be x and y. Then $x^{2} + y^{2}$ is ___

Discussion

5065.	Anne, Benne and Cenne are three friends. Benne takes 2 days more than Cenne to complete the work. If Anne started a work and 3 days later Benne joins him, then the work gets completed in 3 more days. Working together Anne, Benne and Cenne can complete thrice the original work in 6 days. In how many days Benne can complete twice the original work with double the efficiency working alone?
Answer» Anne, Benne and Cenne are three friends. Benne takes 2 days more than Cenne to complete the work. If Anne started a work and 3 days later Benne joins him, then the work gets completed in 3 more days. Working together Anne, Benne and Cenne can complete thrice the original work in 6 days. In how many days Benne can complete twice the original work with double the efficiency working alone?

Discussion

5066.	One year ago, the ratio between A's and B's salary was4:5. The ratio of their individual salaries of last year and present year are3:5and2:3respectively. If their total salaries for the present year is Rs 6800, the present salary of A is
Answer» One year ago, the ratio between A's and B's salary was4:5. The ratio of their individual salaries of last year and present year are3:5and2:3respectively. If their total salaries for the present year is Rs 6800, the present salary of A is

Discussion

5067.	x and y are real numbers satisfying the conditions 2 < x < 3 and -8 < y < - 7. Which of the following expressions will have the least value ?
Answer» x and y are real numbers satisfying the conditions 2 < x < 3 and -8 < y < - 7. Which of the following expressions will have the least value ?

Discussion

5068.	The sum of 6 natural numbers (not necessarily distinct) is 23. Let M denote the positive difference of the maximum and minimum of the LCM of these 6 numbers. Then total number of divisors that divide M2 but doesn't divide M are:
Answer» The sum of 6 natural numbers (not necessarily distinct) is 23. Let M denote the positive difference of the maximum and minimum of the LCM of these 6 numbers. Then total number of divisors that divide $M^{2}$ but doesn't divide M are:

Discussion

5069.	In the league tournament with the conditions as described in the first question, a bookie Charlie follows the following system. In a match between two teams "a” and "b”, the team "a” wins more of their previous matches. If team "a” wins this match, he will pay Rs. 1.5 for every Re. 1 bet on team "a”. If team "b” wins this match, he will pay Rs. 2 for every Re. 1 bet on team "b”. In every match, equal money was bet on both the teams playing in that match. What was Charlie's gain, as a fraction, on the total money that he bet?
Answer» In the league tournament with the conditions as described in the first question, a bookie Charlie follows the following system. In a match between two teams "a” and "b”, the team "a” wins more of their previous matches. If team "a” wins this match, he will pay Rs. 1.5 for every Re. 1 bet on team "a”. If team "b” wins this match, he will pay Rs. 2 for every Re. 1 bet on team "b”. In every match, equal money was bet on both the teams playing in that match. What was Charlie's gain, as a fraction, on the total money that he bet?

Discussion

5070.	In a G-20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharaf.
Answer» In a G-20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharaf.

Discussion

5071.	In the adjoining figure, if AB, SC and TD are perpendicular to BD with the length indicated, then xy is equal to:
Answer» In the adjoining figure, if AB, SC and TD are perpendicular to BD with the length indicated, then $\frac{x}{y}$ is equal to:

Discussion

5072.	If exports to Korea from China forms 80% of the exports to Asia and imports from Korea forms 73% of import from Asia then trade balance of China as defined earlier with Korea is
Answer» If exports to Korea from China forms 80% of the exports to Asia and imports from Korea forms 73% of import from Asia then trade balance of China as defined earlier with Korea is

5072.

If exports to Korea from China forms 80% of the exports to Asia and imports from Korea forms 73% of import from Asia then trade balance of China as defined earlier with Korea is

Answer»

If exports to Korea from China forms 80% of the exports to Asia and imports from Korea forms 73% of import from Asia then trade balance of China as defined earlier with Korea is

Discussion

5073.	Among them who scored the second highest marks?
Answer» Among them who scored the second highest marks?

Discussion

5074.	Find the number of natural number solutions of x1+x2+x3+3x4=15.
Answer» Find the number of natural number solutions of $x_{1} + x_{2} + x_{3} + 3 x_{4} = 15$ .

Discussion

5075.	Three boxes contain 6 red, 4 black; 5 red, 5 black and 4 red, 6 black balls respectively. One of the box is selected at random and a ball is drawn from it. If the ball drawn is red, then the probability that it is drawn from the first bag is k. The value of 10k is___.
Answer» Three boxes contain 6 red, 4 black; 5 red, 5 black and 4 red, 6 black balls respectively. One of the box is selected at random and a ball is drawn from it. If the ball drawn is red, then the probability that it is drawn from the first bag is k. The value of 10k is___.

Discussion

5076.	How to find the square roots using short cut method?
Answer» How to find the square roots using short cut method?

Discussion

5077.	Find the value of 15P4
Answer» Find the value of $^{15} P_{4}$

Discussion

5078.	Details of the number of students applying for CET for engineering Number of students who appeared for the exam as a % of the total no of students who applied for the exam Note: Number of students who secured admission in 1993-94 is 4000. The percentage increase in the number of students who secured admission from 1994-95 to 1999-2000 is
Answer» Details of the number of students applying for CET for engineering Number of students who appeared for the exam as a % of the total no of students who applied for the exam Note: Number of students who secured admission in 1993-94 is 4000. The percentage increase in the number of students who secured admission from 1994-95 to 1999-2000 is

Discussion

5079.	Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1. The same process is applied to S2 to form yet another square S3, and so on. If A1,A2,A3, ……… be the areas and P1,P2,P3, ……… be the perimeters of S1,S2,S3, ……., respectively, then the ratio (P1+P2+P3+P4+…)(A1+A2+A3+A4+…) equals :
Answer» Let $S_{1}$ be a square of side a. Another square $S_{2}$ is formed by joining the mid-points of the sides of $S_{1}$ . The same process is applied to $S_{2}$ to form yet another square $S_{3}$ , and so on. If $A_{1}, A_{2}, A_{3}$ , ……… be the areas and $P_{1}, P_{2}, P_{3}$ , ……… be the perimeters of $S_{1}, S_{2}, S_{3}$ , ……., respectively, then the ratio $\frac{(P_{1} + P_{2} + P_{3} + P_{4} + \dots)}{(A_{1} + A_{2} + A_{3} + A_{4} + \dots)}$ equals :

Discussion

5080.	What would have been Facebook's revenue (in $ million) in its sixth year of operation if the company had matched Google's percentage growth in revenues from the fifth to the sixth year? Choose the option that is nearest to the answer.
Answer» What would have been Facebook's revenue (in $ million) in its sixth year of operation if the company had matched Google's percentage growth in revenues from the fifth to the sixth year? Choose the option that is nearest to the answer.

Discussion

5081.	A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?
Answer» A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?

Discussion

5082.	What is the ratio of the distance travelled by truck A to the distance travelled by truck D?
Answer» What is the ratio of the distance travelled by truck A to the distance travelled by truck D?

Discussion

5083.	If no two children can work simultaneously so that each task is done one after the other, then what will be the least amount a parent has to give to all the tasks done?
Answer» If no two children can work simultaneously so that each task is done one after the other, then what will be the least amount a parent has to give to all the tasks done?

Discussion

5084.	(666……n digits)2+(888……n digits) is equal to
Answer» $(666 \dots \dots n d i g i t s)^{2} + (888 \dots \dots n d i g i t s)$ is equal to

Discussion

5085.	A fire in a building B is reported on telephone to two fire stations P and Q, 20km apart from other on a straight road. P observes that the fire is at an angle of 60∘ to the road and Q observes that it is at an angle of 45∘ to the road. (a) Which station should send its team and how much will this team have to travel? (b) What according to you, are the values displayed by the teams at fire stations P and Q?
Answer» A fire in a building B is reported on telephone to two fire stations P and Q, 20km apart from other on a straight road. P observes that the fire is at an angle of $60^{\circ}$ to the road and Q observes that it is at an angle of $45^{\circ}$ to the road. (a) Which station should send its team and how much will this team have to travel? (b) What according to you, are the values displayed by the teams at fire stations P and Q?

Discussion

5086.	8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed?
Answer» 8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed?

Discussion

5087.	Study the following table carefully to answer these questions: Percent of Marks obtained by six students in six subjects SubjectHistoryGeographyMathsScienceEnglishHindiMax.Marks75751001505060A826659766265B767265847475C567871668670D648068726680E486883885660F607479648085 What are the average marks obtained by all the students in Science out of 150 ?
Answer» Study the following table carefully to answer these questions: Percent of Marks obtained by six students in six subjects $\begin{matrix} S u b j e c t & H i s t o r y & G e o g r a p h y & M a t h s & S c i e n c e & E n g l i s h & H i n d i M a x . M a r k s & 75 & 75 & 100 & 150 & 50 & 60 A & 82 & 66 & 59 & 76 & 62 & 65 B & 76 & 72 & 65 & 84 & 74 & 75 C & 56 & 78 & 71 & 66 & 86 & 70 D & 64 & 80 & 68 & 72 & 66 & 80 E & 48 & 68 & 83 & 88 & 56 & 60 F & 60 & 74 & 79 & 64 & 80 & 85 \end{matrix}$ What are the average marks obtained by all the students in Science out of 150 ?

Discussion

5088.	A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
Answer» A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

Discussion

5089.	The product of two 2 two digt numbers is 2160.HCF is 12 find the numbers
Answer» The product of two 2 two digt numbers is 2160.HCF is 12 find the numbers

Discussion

5090.	Arjun can kill a bird once in 3 shots. On the assumption that he fires 3 shots, the probability that the bird is killed is x27. Find the value of x. ___
Answer» Arjun can kill a bird once in 3 shots. On the assumption that he fires 3 shots, the probability that the bird is killed is $\frac{x}{27}$ . Find the value of x. ___

Discussion

5091.	Which branch has the lowest average Profit?
Answer» Which branch has the lowest average Profit?

Discussion

5092.	A shopkeeper keeps 100 marbles in two boxes, A and B, such that Box A contains only red and Box B contains only green marbles. Barring an equal number of marbles from each box, he sold all the others and earned Rs. 25 and Rs. 15 from Box A and Box B respectively. Later, he sold half of the remaining marbles. His total earning from all the transactions accumulated to Rs. 45. What is the cost of each marble - red or green.?
Answer» A shopkeeper keeps 100 marbles in two boxes, A and B, such that Box A contains only red and Box B contains only green marbles. Barring an equal number of marbles from each box, he sold all the others and earned Rs. 25 and Rs. 15 from Box A and Box B respectively. Later, he sold half of the remaining marbles. His total earning from all the transactions accumulated to Rs. 45. What is the cost of each marble - red or green.?

Discussion

5093.	Is the thereon like SSS, SAS, AAA ,AA is important for the purpose of exam?
Answer» Is the thereon like SSS, SAS, AAA ,AA is important for the purpose of exam?

Discussion

5094.	Step 2 of an input is:east 71 39 47 hold goal 29 more Which of the following is definitely the input?
Answer» Step 2 of an input is:east 71 39 47 hold goal 29 more Which of the following is definitely the input?

5094.

Step 2 of an input is:east 71 39 47 hold goal 29 more Which of the following is definitely the input?

Answer»

Step 2 of an input is:east 71 39 47 hold goal 29 more

Which of the following is definitely the input?

Discussion

5095.	In how many ways can Rs. 18.75 be paid in exactly 85 coins consisting of 50-paisa, 25-paisa and 10-paisa coins?
Answer» In how many ways can Rs. 18.75 be paid in exactly 85 coins consisting of 50-paisa, 25-paisa and 10-paisa coins?

Discussion

5096.	In class V, there are 14 boys and 7 girls. The teacher wants to select either a boy or a girl as the class leader. In how many ways can the teacher select the class leader?21
Answer» In class V, there are 14 boys and 7 girls. The teacher wants to select either a boy or a girl as the class leader. In how many ways can the teacher select the class leader? 21

Discussion

5097.	Prove that the equal chords of a circle are equidistant from the center.
Answer» Prove that the equal chords of a circle are equidistant from the center.

Discussion

5098.	If the export revenue from Mainframe increased by 121% in 2000 over that in 1999, what percentage of the export revenue in 1999 was accounted by Mainframe?
Answer» If the export revenue from Mainframe increased by 121% in 2000 over that in 1999, what percentage of the export revenue in 1999 was accounted by Mainframe?

Discussion

5099.	Two circles touch internally at point P and a chord AB of the circle of larger radius intersects the other circle in C and D. Which of the following holds good?
Answer» Two circles touch internally at point P and a chord AB of the circle of larger radius intersects the other circle in C and D. Which of the following holds good?

Discussion

5100.	Show that any positive odd integer is of form (6m+1) or (6m+3) or (6m+5), where m is some integer.
Answer» Show that any positive odd integer is of form (6m+1) or (6m+3) or (6m+5), where m is some integer.

Discussion

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Q38. In a certain brick wall, each row of bricks above the bottom row contains one less brick than the row just below it. If there are 5 rows in all and a total of 75 bricks in the wall, how many bricks does the bottom row contain?

Ajay and his wife Kajol appear in an interview for two vacancies in the same post. The probability of Ajay's selection is 17 and that of his wife Kajol's selection is 15. What is the probability that only one of them will be selected?

The average weight of a b and c is 45kg. if the average weight of A and B be 40kg and that of B and C be 43kg then find the weight of B

Anita, Sunita, Ram and Raman scored 89, 87, 90 and 55 marks (out of 100) respectively in an exam. Who scored the maximum percentage and how much is that value?

x2+px+q=0 in the equation there r α and β, show 1α+β and (1α+1β) in which equation is pqx2+(p2+q)x+p=0

A toy is in the shape of a hemisphere surmounted by a cone. If the radius of the base of the cone is 3cm and height is 4cm, the total surface area of the toy is :

A student took fine papers in an examination where the full marks were the same for each paper. His marks in these papers were 6:7:8:9. He obtained (35) part of the total full marks. Then the numbers of papers in which he got more than 50 marks is ___

What is the volume of 2g O2 at 0 degree centigrade and 760 mm pressure of Hg?

Find the 300th term in the series A26, B25, B25, C24, C24, C24 , D23, ……

If a,b,c are the lengths of the perpendiculars dropped from a point inside on an equilateral triangle of side "p” on its sides, then find a+b+c

Let two adjacent sides of a parallelogram be a and b while the diagonals be x and y. Then x2+y2 is ___

One year ago, the ratio between A's and B's salary was4:5. The ratio of their individual salaries of last year and present year are3:5and2:3respectively. If their total salaries for the present year is Rs 6800, the present salary of A is

x and y are real numbers satisfying the conditions 2 &lt; x &lt; 3 and -8 &lt; y &lt; - 7. Which of the following expressions will have the least value ?

The sum of 6 natural numbers (not necessarily distinct) is 23. Let M denote the positive difference of the maximum and minimum of the LCM of these 6 numbers. Then total number of divisors that divide M2 but doesn't divide M are:

In a G-20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharaf.

In the adjoining figure, if AB, SC and TD are perpendicular to BD with the length indicated, then xy is equal to:

If exports to Korea from China forms 80% of the exports to Asia and imports from Korea forms 73% of import from Asia then trade balance of China as defined earlier with Korea is

Among them who scored the second highest marks?

Find the number of natural number solutions of x1+x2+x3+3x4=15.

Three boxes contain 6 red, 4 black; 5 red, 5 black and 4 red, 6 black balls respectively. One of the box is selected at random and a ball is drawn from it. If the ball drawn is red, then the probability that it is drawn from the first bag is k. The value of 10k is___.

How to find the square roots using short cut method?

Find the value of 15P4

What would have been Facebook's revenue (in $ million) in its sixth year of operation if the company had matched Google's percentage growth in revenues from the fifth to the sixth year? Choose the option that is nearest to the answer.

What is the ratio of the distance travelled by truck A to the distance travelled by truck D?

If no two children can work simultaneously so that each task is done one after the other, then what will be the least amount a parent has to give to all the tasks done?

(666……n digits)2+(888……n digits) is equal to

8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed?

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

The product of two 2 two digt numbers is 2160.HCF is 12 find the numbers

Arjun can kill a bird once in 3 shots. On the assumption that he fires 3 shots, the probability that the bird is killed is x27. Find the value of x. ___

Which branch has the lowest average Profit?

Is the thereon like SSS, SAS, AAA ,AA is important for the purpose of exam?

Step 2 of an input is:east 71 39 47 hold goal 29 more Which of the following is definitely the input?

In how many ways can Rs. 18.75 be paid in exactly 85 coins consisting of 50-paisa, 25-paisa and 10-paisa coins?

In class V, there are 14 boys and 7 girls. The teacher wants to select either a boy or a girl as the class leader. In how many ways can the teacher select the class leader?21

Prove that the equal chords of a circle are equidistant from the center.

If the export revenue from Mainframe increased by 121% in 2000 over that in 1999, what percentage of the export revenue in 1999 was accounted by Mainframe?

Two circles touch internally at point P and a chord AB of the circle of larger radius intersects the other circle in C and D. Which of the following holds good?

Show that any positive odd integer is of form (6m+1) or (6m+3) or (6m+5), where m is some integer.

x and y are real numbers satisfying the conditions 2 < x < 3 and -8 < y < - 7. Which of the following expressions will have the least value ?