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# Which of the following is NOT prime?

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Math Expert
Joined: 02 Sep 2009
Posts: 64068
Which of the following is NOT prime?  [#permalink]

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29 Jan 2015, 07:47
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Difficulty:

95% (hard)

Question Stats:

26% (01:44) correct 74% (01:51) wrong based on 155 sessions

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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

Kudos for a correct solution.

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Posts: 64068
Re: Which of the following is NOT prime?  [#permalink]

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02 Feb 2015, 03:08
1
2
Bunuel wrote:
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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

None of our easy tests (divisibility by 3, divisibility by 5, etc.) eliminate any options, so let's try something else. The first three look like gibberish, so we'll begin with the last two. They sure look CLOSE to friendly numbers, don't they? 3,999,991 = 4,000,000 - 9, for instance ... and that's the same thing as 2000^2−32 ... which factors as the difference of squares into (2000+3)(2000-3), or 2003 * 1997. Since 3,999,991 has at least TWO factors OTHER THAN 1 and itself, it's not prime, and we're done!

Note that 9,999,991 looks very similar, but when you try to write it in terms of powers of 10 the methodology breaks down. 10,000,000 - 9 looks similar, but 10,000,000 = 10^7, which with an odd power doesn't break down cleanly into Difference of Squares and therefore does not work.
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Re: Which of the following is NOT prime?  [#permalink]

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10 Feb 2015, 13:02
Bunuel wrote:
Bunuel wrote:
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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

None of our easy tests (divisibility by 3, divisibility by 5, etc.) eliminate any options, so let's try something else. The first three look like gibberish, so we'll begin with the last two. They sure look CLOSE to friendly numbers, don't they? 3,999,991 = 4,000,000 - 9, for instance ... and that's the same thing as 2000^2−32 ... which factors as the difference of squares into (2000+3)(2000-3), or 2003 * 1997. Since 3,999,991 has at least TWO factors OTHER THAN 1 and itself, it's not prime, and we're done!

Note that 9,999,991 looks very similar, but when you try to write it in terms of powers of 10 the methodology breaks down. 10,000,000 - 9 looks similar, but 10,000,000 = 10^7, which with an odd power doesn't break down cleanly into Difference of Squares and therefore does not work.

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!
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Re: Which of the following is NOT prime?  [#permalink]

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10 Feb 2015, 18:45
1
Ralphcuisak wrote:
Bunuel wrote:
Bunuel wrote:
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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

None of our easy tests (divisibility by 3, divisibility by 5, etc.) eliminate any options, so let's try something else. The first three look like gibberish, so we'll begin with the last two. They sure look CLOSE to friendly numbers, don't they? 3,999,991 = 4,000,000 - 9, for instance ... and that's the same thing as 2000^2−32 ... which factors as the difference of squares into (2000+3)(2000-3), or 2003 * 1997. Since 3,999,991 has at least TWO factors OTHER THAN 1 and itself, it's not prime, and we're done!

Note that 9,999,991 looks very similar, but when you try to write it in terms of powers of 10 the methodology breaks down. 10,000,000 - 9 looks similar, but 10,000,000 = 10^7, which with an odd power doesn't break down cleanly into Difference of Squares and therefore does not work.

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!

$$3,999,991 = 4000000 - 9 = 2000^2 - 3^2 = 2003 * 1997$$

Its not a prime number

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Joined: 05 Mar 2015
Posts: 936
Which of the following is NOT prime?  [#permalink]

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14 Jan 2016, 04:17
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????????
Math Expert
Joined: 02 Aug 2009
Posts: 8584
Re: Which of the following is NOT prime?  [#permalink]

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14 Jan 2016, 06:24
Bunuel wrote:
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

Kudos for a correct solution.

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..
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Re: Which of the following is NOT prime?  [#permalink]

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14 Jan 2016, 22:23
1
rohit8865 wrote:
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????????

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.

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Re: Which of the following is NOT prime?  [#permalink]

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25 May 2016, 11:13
Bunuel wrote:
Bunuel wrote:
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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

None of our easy tests (divisibility by 3, divisibility by 5, etc.) eliminate any options, so let's try something else. The first three look like gibberish, so we'll begin with the last two. They sure look CLOSE to friendly numbers, don't they? 3,999,991 = 4,000,000 - 9, for instance ... and that's the same thing as 2000^2−32 ... which factors as the difference of squares into (2000+3)(2000-3), or 2003 * 1997. Since 3,999,991 has at least TWO factors OTHER THAN 1 and itself, it's not prime, and we're done!

Note that 9,999,991 looks very similar, but when you try to write it in terms of powers of 10 the methodology breaks down. 10,000,000 - 9 looks similar, but 10,000,000 = 10^7, which with an odd power doesn't break down cleanly into Difference of Squares and therefore does not work.

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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Re: Which of the following is NOT prime?  [#permalink]

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25 May 2016, 19:10
1
rhine29388 wrote:
Bunuel wrote:
Bunuel wrote:
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

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

None of our easy tests (divisibility by 3, divisibility by 5, etc.) eliminate any options, so let's try something else. The first three look like gibberish, so we'll begin with the last two. They sure look CLOSE to friendly numbers, don't they? 3,999,991 = 4,000,000 - 9, for instance ... and that's the same thing as 2000^2−32 ... which factors as the difference of squares into (2000+3)(2000-3), or 2003 * 1997. Since 3,999,991 has at least TWO factors OTHER THAN 1 and itself, it's not prime, and we're done!

Note that 9,999,991 looks very similar, but when you try to write it in terms of powers of 10 the methodology breaks down. 10,000,000 - 9 looks similar, but 10,000,000 = 10^7, which with an odd power doesn't break down cleanly into Difference of Squares and therefore does not work.

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

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.
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Re: Which of the following is NOT prime?  [#permalink]

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09 Jun 2018, 00:27
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Re: Which of the following is NOT prime?   [#permalink] 09 Jun 2018, 00:27