XAT 2019 — QA & DI Question 20
We have two unknown positive integers m and n, whose product is less than 100.
There are two additional statement of facts available:
- mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
- 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?
Answer & solution
- A
Statements 1 and 2 together are not suï¬cient, and additional data is needed to answer the question.
Both statements taken together are suï¬cient to answer the question, but neither statement alone is suï¬cient.
- C
Each statement alone is suï¬cient to answer the question.
- D
Statement 2 alone is suï¬cient, but statement 1 alone is not suï¬cient to answer the question.
- E
Statement 1 alone is suï¬cient, but statement 2 alone is not suï¬cient to answer the question.
Looking at the initial statement , we know that mn < 100.
Looking at statement I ,we get to know that the product mn has to be a multiple of 10 since it is divisible by 6 consecutive integers .So the product can be either 10, 20, 30 ….90
Now of all these numbers only 60 is divisible by 6 consecutive numbers i.e. numbers 1 to 6.60 can be expressed as a product of 2 nos. in the following ways : 1 × 60, 2 × 30, 3 × 20, 4 × 15, 5 × 12, 6 ×10
So from statement I alone we cannot determine values of m and n. Looking at statement II alone determine values of m and n as the only information provided to us is that “m + n” is a perfect square. So we can have numerous possibilities for m and n [e.g (7, 9), (2, 7), (1, 3) etc ]
Combining both statements out of (1, 60), (2, 30), (3, 20), (4,15), (5, 12), (6, 10), the only pair of values such that “m+n” is a perfect square is (6, 10). Hence both statements are required to answer the question.
Hence, option (b).