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Math Expert V
Joined: 02 Sep 2009
Posts: 58335
If x and y are different prime numbers, is x = 5?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:08) correct 25% (01:13) wrong based on 82 sessions

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If x and y are different prime numbers, is x = 5?

(1) The average (arithmetic mean) of x, y, and 4 is 4.
(2) x > y.

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Manager  B
Joined: 23 Oct 2017
Posts: 61
Re: If x and y are different prime numbers, is x = 5?  [#permalink]

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Mean of x,y,4 = 4
x+y+4=12
x+y=8 implying 2 pairs x,y = 3,5 or 5,3
to determine wheter x is 5, need stmt 2 which says x>y => x=5 & y=3
Intern  B
Joined: 16 Apr 2017
Posts: 12
Re: If x and y are different prime numbers, is x = 5?  [#permalink]

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Ans: E...
1. x+y+4=12
x+y=8
x can be any value from 1 to 7...
Not sufficient.
2. Don't know values.
Not sufficient.
Combining 1&2:
x can be 5,6 or 7....
Not sufficient.

Sent from my ONEPLUS A5010 using GMAT Club Forum mobile app
Intern  B
Joined: 06 Dec 2017
Posts: 14
Re: If x and y are different prime numbers, is x = 5?  [#permalink]

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pu230163 wrote:
Ans: E...
1. x+y+4=12
x+y=8
x can be any value from 1 to 7...
Not sufficient.
2. Don't know values.
Not sufficient.
Combining 1&2:
x can be 5,6 or 7....
Not sufficient.

X,Y are "Different prime numbers" so only two possible values 5&3 or 3 & 5
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1431
Location: India
Re: If x and y are different prime numbers, is x = 5?  [#permalink]

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pu230163 wrote:
Ans: E...
1. x+y+4=12
x+y=8
x can be any value from 1 to 7...
Not sufficient.
2. Don't know values.
Not sufficient.
Combining 1&2:
x can be 5,6 or 7....
Not sufficient.

Sent from my ONEPLUS A5010 using GMAT Club Forum mobile app

Hi

Its given that x and y are distinct prime numbers. So we can not include all cases from 1 to 7. Only possibilities would be (from statement 1): x=3, y=5 OR x=5, y=3
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7999
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x and y are different prime numbers, is x = 5?  [#permalink]

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Bunuel wrote:
If x and y are different prime numbers, is x = 5?

(1) The average (arithmetic mean) of x, y, and 4 is 4.
(2) x > y.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations,C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):
We have x + y = 8 from the condition 1).
Since x, y are prime numbers, x = 3, y = 5 or x = 5, y = 3.
From the condition 2), x = 5 and y = 3.
Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since we have two solutions x = 3, y = 5 or x = 5, y = 3, the condition 1) only is not sufficient.

Condition 2)
Since we have a bunch of solutions x = 3, y = 2 or x = 5, y = 2, for example, the condition 2) only is not sufficient.

Therefore, the answer is C.

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.
_________________ Re: If x and y are different prime numbers, is x = 5?   [#permalink] 04 Jan 2018, 23:31
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