Question of the day - 1

Q ) How many pair of natural numbers are such that difference between their squares is 39?


Options:

• 1
• 2
• 3
• 4

Now before you proceed further, just try to solve it by your own. Kindly post your solution in comment area. There are always many different ways in which question can be cracked but here we will see the shortest and most efficient method. If you have any better method, your suggestions are welcome. 

Solution:

Natural numbers are all positive numbers greater then 0.

A² - B² = 39
(A-B) (A+B) = 39

Now 39 can be factorized as

• 1 * 39
• 3 * 13
• 13 * 3
• 39 * 1

So we get for cases:

Case 1 :

A - B = 1

A + B = 39

So A = 20 and B = 19

Case 2:

A - B = 39

A + B = 1

So A = 20 and B = -19

Case 3:

A - B = 3

A + B = 13

So A = 8 and B = 5

Case 4:

A - B = 13

A + B = 3

A = 8 and B = -5

Now from all the above four cases, only two are positive pairs. So our answer is two. Option 2.

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Question of the day!

Hi,

Almost every alternate day I post a session on vocabulary. And I guess its helping you out. But to prepare a quant concept session in one day is bit difficult. I have come up with an idea. I will post one quant question every day. The question will pertain purely to simple but profound logic. This will help you develop think out of the box ability which is must for cracking exams like CAT. Moreover, there are many website that provide "question of the day" facility. But most of them provide the questions of the kind that are almost not asked in actual exams. Before using any source, you must realize that what it provides and is it relevant with the exam. If you see the past years question papers, you will see that not even a single question can be solved with the formula that we have learned in our school days. Yes, formula can be used as a tool but at a same time logic is must. And that is what we shall develop here. Many books and websites provide questions that are typical maths problems. If you are practicing those sums then you are actually doing nothing. 

I will try to provide you an idea of what kind of logic you may need to crack the quant part of the CAT. Hope this will help you. All the best!