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GRE 1: Q169 V154 If x are y are positive integers, what is the value of x+y  [#permalink]

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If x are y are positive integers, what is the value of x+y?
(1) x and y are consecutive prime numbers
(2) x-y=1

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Re: If x are y are positive integers, what is the value of x+y  [#permalink]

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If x are y are positive integers, what is the value of x+y?
(1) x and y are consecutive prime numbers
(2) x-y=1

from 1- 2,3 are consecutive prime nos.
from2- many possibilities are there

hence A
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Re: If x are y are positive integers, what is the value of x+y  [#permalink]

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1
s1d1 wrote:
If x are y are positive integers, what is the value of x+y?
(1) x and y are consecutive prime numbers
(2) x-y=1

from 1-2,3 are consecutive prime nos.
from2- many possibilities are there

hence A

The highlighted is not true. 3, 5 are consecutive prime numbers, 7, 11 are consecutive prime numbers

(1) or (2) can't lead to value of x + y.

Combine (1) and (2): only $$(x,y)=(3,2)$$ sufficient.

The answer is C.

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Re: If x are y are positive integers, what is the value of x+y  [#permalink]

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1
Tip: Consecutive prime numbers doesn't imply only on the pair (2,3).
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Re: If x are y are positive integers, what is the value of x+y  [#permalink]

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stonecold wrote:
If x are y are positive integers, what is the value of x+y?
(1) x and y are consecutive prime numbers
(2) x-y=1

x,y > 0
x + y = ?

1) x, y -> consecutive primes
x = 2, y = 3
x + y = 5
x = 3, y = 5
x + y = 8
Insufficient.

2) x = y + 1
y = 1, x = 2
y = 2, x = 3
Insufficient.

1+2)
x = y + 1 & x,y are consecutive primes.
=> y = 2, x = 3
Sufficient.

C is the answer.
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Re: If x are y are positive integers, what is the value of x+y  [#permalink]

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If x are y are positive integers, what is the value of x+y?

(1) x and y are consecutive prime numbers

x and y can take values such as:

2, 3 = x + y = 2 + 3 = 5
3, 5 = x + y = 3 + 5 = 8
5, 7 = x + y = 5 + 7 = 12

As we are getting multiple values, this information is not sufficient.

Hence, (1) ===== is NOT SUFFICIENT

(2) $$x-y=1$$

Once again, x and y can take values such as:

3, 2 = x + y = 3 + 2 = 5
5, 4 = x + y = 5 + 4 = 9
7, 6 = x + y = 7 + 6 = 13

As we are getting multiple values, this information is not sufficient.

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

x and y are consecutive prime numbers and $$x-y=1$$

With above information, there is only one possibility

x = 3

y = 2

3 - 2 = 1

Hence, (1) & (2) ===== is SUFFICIENT

Hence, Answer is C
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Re: If x are y are positive integers, what is the value of x+y  [#permalink]

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stonecold wrote:
If x are y are positive integers, what is the value of x+y?

(1) x and y are consecutive prime numbers
(2) x - y = 1

Target question: What is the value of x+y?

Given: x are y are positive integers

Statement 1: x and y are consecutive prime numbers
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 3 (two consecutive primes), in which case x + y = 2 + 3 = 5
Case b: x = 19 and y = 23 (two consecutive primes), in which case x + y = 19 + 23 = 42
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read this article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x - y = 1
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 3 and y = 2, in which case x + y = 3 + 2 = 5
Case b: x = 5 and y = 4, in which case x + y = 5 + 4 = 9
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x and y are consecutive primes
Statement 2 tells us that x and y differ by 1
If x and y differ by 1, then one number is ODD and the other is EVEN
Since there is only one EVEN prime number (2), then it must be the case that y = 2 and x = 3, in which case x + y = 3 + 2 = 5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: If x are y are positive integers, what is the value of x+y  [#permalink]

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_________________ Re: If x are y are positive integers, what is the value of x+y   [#permalink] 06 Jun 2019, 03:51
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