Xavier Aptitude Test 2019 Paper

Question : 67 of 98

Marks: +1, -0

We have two unknown positive integers m and n, whose product is less than 100.
There are two additional statement of facts available:
1. mn is divisible by six consecutive integers

\{j,j+1,...,j+5\}

2. m + n is a perfect square.
Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.

Validate

Solution:

L C M of 1,2 ,3 ,4 ,5 and 6 = 60
LCM of 2 , 3 ,4 ,5 ,6 and 7 = 420
Since, mn < 100
∴ LCM = 60
60 → 1 × 60, 2 × 3 0, 3 × 20, 4 × 15, 5 × 12, 6 × 10
Now,

6 + 10 = 16 = (4)^2

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