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# Is the sum of the integers x and y a prime number?

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Joined: 02 Sep 2009
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Is the sum of the integers x and y a prime number?  [#permalink]

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11 Oct 2019, 01:50
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25% (medium)

Question Stats:

82% (01:10) correct 18% (00:58) wrong based on 22 sessions

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Is the sum of the integers x and y a prime number?

(1) x is an even prime number.
(2) y is a prime number between 10 and 20.

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11 Oct 2019, 08:59
We are required to check whether x+y is a prime number.

(1) 2 is the only even prime number, so x=2
However, we don't know the value of y.
Thus, insufficient.

(2) As per this statement, y=13,17, or 19.
Also, we don't know the value of x.
Thus, insufficient.

From (1) and (2) together, x+y=15,19,or 21.
Thus, insufficient.

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Re: Is the sum of the integers x and y a prime number?  [#permalink]

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11 Oct 2019, 09:26
Bunuel wrote:
Is the sum of the integers x and y a prime number?

(1) x is an even prime number.
(2) y is a prime number between 10 and 20.

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Since we have 2 variables (x and y) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
If x = 2 and y = 11, then x + y = 13 is a prime number and the answer is 'yes'.
If x = 2 and y = 13, then x + y = 15 is not a prime number and the answer is 'no'.

Since both conditions together do not yield a unique solution, they are not sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Is the sum of the integers x and y a prime number?  [#permalink]

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11 Oct 2019, 09:49
Q. Is (x+y) prime?

(1) x is an even prime number, so x=2.
We don't know y value.
NOT SUFFICIENT.

(2) y is a prime number between 10 and 20, so y can be 11,13,17, or 19.
We don't know x value.
NOT SUFFICIENT.

(1)+(2),
(x+y) can be 13,15,19,or 21. (x+y) may or may not be a prime number.
NOT SUFFICIENT

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Re: Is the sum of the integers x and y a prime number?  [#permalink]

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11 Oct 2019, 19:42
Is the sum of the integers x and y a prime number?
x + y = prime ??

(1) x is an even prime number.
x = 2
As y is unknown so it can take any value. Thus

INSUFFICIENT.

(2) y is a prime number between 10 and 20.

Possible values of y are 11, 13 17 and 19.
Since x is unknown and it can take any value, statement is not sufficient.

INSUFFICIENT.

Together 1 and 2
Possible values of 'x + y' are 13, 1, 19 and 21. So two values are prime and two are not.Hence

INSUFFICIENT.

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Re: Is the sum of the integers x and y a prime number?   [#permalink] 11 Oct 2019, 19:42
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