Four numbers whose sum is 40 and sum of their squares is 480. What are the four numbers?(a) 4, 8, 12, and -16(b) 4, 8, 12, and 16(c) -4, 8, 12, and 16(d) 4, -8, 12, and 16The question was asked during an online interview.Asked question is from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10

Four numbers whose sum is 40 and sum of their squares is 480. What are

1.	Four numbers whose sum is 40 and sum of their squares is 480. What are the four numbers?(a) 4, 8, 12, and -16(b) 4, 8, 12, and 16(c) -4, 8, 12, and 16(d) 4, -8, 12, and 16The question was asked during an online interview.Asked question is from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10
Answer» RIGHT choice is (b) 4, 8, 12, and 16 To elaborate: LET the four NUMBERS be (a + 3d), (a + d), (a – 3d), (a – d). Sum of the four numbers is 40. a + 3d + a + d + a – 3d + a – d = 40 4a = 40 a = 10 Sum of their SQUARES is 480. (a + 3d)^2 + (a + d)^2 + (a – 3d)^2 + (a – d)^2 = 480 4a^2 + 20d^2 = 480 10^2 + 5d^2 = 120 100 + 5d^2 = 120 5d^2 = 20 d^2 = 4 d = 2, -2 Hence the four numbers are 4, 8, 12, and 16.

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