Which of the following is NOT prime?

So this is what went through my mind when I saw this question:

How do we find out whether a number n is prime? It must not be divisible by any prime number from 2 to \(\sqrt{n}\). But these numbers are huge. Obviously we cannot check for their square root, let alone for all primes in between. I ensured that all numbers end in 1/3/7/9 and I looked for divisibility by 3 - nothing.
It was obvious that the trick lies somewhere else. Options (A), (B) and (C) seemed random enough. Option (D) is something we come across often. The moment we see this, we change it to a number ending in many 0s minus 9. We see such numbers often when dealing with algebraic identities. 9 is a perfect square. Seems like we got what we wanted.
3,999,991 = 4,000,000 - 9 = (2000)^2 - 3^2
So this number is a product of two numbers other than 1 and itself. This means it is not prime. This must be the answer.

Let's take a look at (E) too.
9,999,991 = 10,000,000 - 9
Here the difference is that 10,000,000 is not a perfect square. It has odd number of 0s. So this would be a prime number.

Answer (D)

We are not ruling out options (A), (B) and (C) - we are ignoring them for the time being and jumping straight to (D) because it makes sense to us. We know how to deal with numbers in options (D) and (E) so we do that first. If we wouldn't have been able to arrive at an answer from them, we would have wrestled with (A), (B) and (C) and tried to find some logic in them.

Hi Bunuel,

How is 4,000,000 - 9=4000,000-32(2000^2-32)? i think it is (2000^2-3^2).Please correct me if i am missing something here.

TIA!

Which of the following is NOT prime?

A. 1,556,551
B. 2,442,113
C. 3,893,257
D. 3,999,991
E. 9,999,991

Can anyone help me getting breakup of choices B & C????

I could only think upto the combination 4 digit no must contain unit digit as 2 or 3 ,so that it can be written as a^2- b^2????????

Hi,
I think a very very poor Q, by all standards..
There could have been better ways to test students on usage of a^2-b^2, than putting it across through such gibberish numbers, surprisingly the source too claims it gibberish in its solution..
Next time some source will come up with some more gibberish number and a number 809951..
solution:- 809951 looks better than other numbers, since it has 99 in it...
lets see ..
it can be converted into 900^2-7^2...
so here we have the answer..

tried the q in many ways and thought would learn something new but found a solution talking of gibberish numbers..
real disappointing Q..

A genuine query
On what basis are we ruling out options A,B and C?
just because they seem to be gibberish doesn't mean we can reject them straightforward without applying any logic to it

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