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x and y are integers less than 60 such that x is equal to the sum of

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Bunuel
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x and y are integers less than 60 such that x is equal to the sum of [#permalink] New post   11 Mar 2022, 06:45
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68% (02:38) correct 32% (02:43) wrong based on 108 sessions
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x and y are integers less than 60 such that x is equal to the sum of the squares of two distinct prime numbers, and y is a multiple of 17. Which of the following could be the value of x – y?

А. –19
B. –7
C. 0
D. 4
E. 9
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C
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Charli08
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Re: x and y are integers less than 60 such that x is equal to the sum of [#permalink] New post   11 Mar 2022, 16:38
x&y < 60

x = a^2 + b^2 (where a & b are prime)

y = 17c (where c is an integer c>= 1)

Question: x-y = ?

There are quite a few options for x and even more for x-y. In such cases I would look at the rules for each value for a clue. It says x is the sum of two distinct primes. The one special type of prime number is 2 as it is even and the GMAT might be trying to catch you out on this. Now if we try using 2 as one of our options and the next biggest prime to test:

x = 2^2 + 3^2 = 13
y = 17

17 - 13 = 4

Hence we get our answer. If we didn't I would probably skip the question as it might take more than 2 minutes.

==> D
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lammy323
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Re: x and y are integers less than 60 such that x is equal to the sum of [#permalink] New post   11 Mar 2022, 18:02
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The user above makes the mistake of doing y-x rather than x-y.

If x = 3^2 + 5^2 = 34 and y = 2*17 = 34

Then our answer is 34-34=0 (C)
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Preeeeeetika
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Re: x and y are integers less than 60 such that x is equal to the sum of [#permalink] New post   24 Mar 2022, 23:15
Charli08 wrote:
x&y < 60

x = a^2 + b^2 (where a & b are prime)

y = 17c (where c is an integer c>= 1)

Question: x-y = ?

There are quite a few options for x and even more for x-y. In such cases I would look at the rules for each value for a clue. It says x is the sum of two distinct primes. The one special type of prime number is 2 as it is even and the GMAT might be trying to catch you out on this. Now if we try using 2 as one of our options and the next biggest prime to test:

x = 2^2 + 3^2 = 13
y = 17

17 - 13 = 4

Hence we get our answer. If we didn't I would probably skip the question as it might take more than 2 minutes.

==> D



Hey Charli08,
The question asks specifically for x-y
You seem to have calculated y-x instead, resulting in a positive 4
whereas, x-y would result in -4

After calculation (keeping all constraints in mind) we get:
x=13 or 34
y= 17 or 34 or 52

possible values of x-y = -4 or 0 or -52
the only one in the options is (C) 0
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Re: x and y are integers less than 60 such that x is equal to the sum of [#permalink] New post   02 May 2023, 00:44
x and y < 60

x= (prime)^2 + (prime)^2
y= 17 (a) {multiple of 17, a is just to denote that}

Some prime Numbers for reference- 2,3,5,7,11,13,17

Done by mixing up prime square and adding up
x= 13, 29, 34, 53, 58, 124, 130
y= 17,34,51,68,85,102,119

both x and y have 34. Thus x-y = 0.

Hence C.

If lets say 0 was not to be the answer, then I would have done x-y by mixing and matching.
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Re: x and y are integers less than 60 such that x is equal to the sum of [#permalink]
02 May 2023, 00:44
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