1.

1). If the data given in the statement I alone is sufficient to answer the question whereas the data given in statement II alone is not sufficient to answer the question.2). If the data given in the statement II alone is sufficient to answer the question whereas the data given in statement I alone is not sufficient to answer the question.3). If the data in either statement I alone or in statement II alone is sufficient to answer the question.4). If the data in either statement I & II is not sufficient to answer the question.

Answer»

Let the 2-digit number be X Y.

∴ This number can be represented as 10 X + Y.

By checking each statement individually-

Statement I-

The average of 2 individual DIGITS is 2 more than their addition.

As average of 2 digits = (X + Y)/ 2

As per statement I-

(X + Y)/2 = X + Y - 2

∴ X + Y = (X + Y - 2) × 2

∴ X + Y = 2 X + 2Y - 4

∴ X + Y = 4 ---- (1)

But statement I fail to give individual digits.

∴ Statement I alone can’t figure out 2-digit number.

Statement II-

The difference between 2 digits is 2 and 10th place digit is HIGHER than unit’s place digit.

∴ X – Y = 2 ---- (2)

But statement II fail to give individual digits.

∴ Statement II alone can’t figure out 2-digit number.

Combining information of both results-

X + Y = 4

& X – Y = 2

Adding both results-

(X + Y) + (X - Y) = 4 + 2

∴ 2 X = 6

∴ X = 3

Putting VALUE of X in 1st result-

X + Y = 4

3 + Y = 4

∴ Y = 1

∴ 2-digit number is 31.

∴ Both STATEMENTS are essential to find 2-digit numbers.


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