# CAT 2019 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Quants Questions | Question 22

Type in the answer or TITA type questions are often on the trickier side of the spectrum as you do not have options to cross-check your answer with! Hence, it is vital that you practice enough number of questions so that you are comfortable around such questions if the appear in the CAT Question Paper this year(which is a very likely situation!). What better than practicing actual CAT previous year paper and analyzing your solution to understand where you stand in your online CAT preparation and alter your preparation strategy accordingly? Start with this Number Theory question from CAT 2019 Question Paper Slot 2!

Question 22 : How many pairs (m,n) of positive integers satisfy the equation the equation m2 + 105 = n2? [TITA]

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### Explanatory Answer

We know that m2 + 105 = n2
105 = n2 - m2
105 = (n+m) (n-m)
105 can be written as 3 x 5 x 7, which can be written in 4 ways
(1 x 105), (3 x 35), (5 x 21), (7 x 15) can be the possible values of m and n respectively
4 pairs

The question is "How many pairs (m,n) of positive integers satisfy the equation the equation m2 + 105 = n2? [TITA] "

##### Hence, the answer is 4

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