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Math Expert V
Joined: 02 Sep 2009
Posts: 58320
What is the value of integer x?  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 48% (01:55) correct 52% (02:01) wrong based on 279 sessions

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What is the value of integer x?

(1) The sum of all the unique factors of x is 24.

(2) 10 < x < 20

Kudos for a correct solution.

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Math Expert V
Joined: 02 Aug 2009
Posts: 7953
Re: What is the value of integer x?  [#permalink]

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ans E...
1) there are more than possible value of x....23 ,15 ..insufficient
2) values could be from 11 to 19... insufficient
combined, there are still more than one value satisfying x...14,15..insufficient
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Manager  Joined: 27 Dec 2013
Posts: 199
Re: What is the value of integer x?  [#permalink]

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+1 for E. Bunuel post OA, please.

the numbers are 14 and 15; hence, we cannot single one number.

Bunuel wrote:
What is the value of integer x?

(1) The sum of all the unique factors of x is 24.

(2) 10 < x < 20

Kudos for a correct solution.

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Kudos to you, for helping me with some KUDOS.
Intern  Joined: 09 Apr 2013
Posts: 31
Schools: Booth '16
Re: What is the value of integer x?  [#permalink]

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Statement 1 - not sufficient - 14, 15, 23 etc....

statement 2 - not sufficient - 14, 15
Senior Manager  B
Joined: 28 Feb 2014
Posts: 291
Location: United States
Concentration: Strategy, General Management
Re: What is the value of integer x?  [#permalink]

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1
Bunuel wrote:
What is the value of integer x?

(1) The sum of all the unique factors of x is 24.

(2) 10 < x < 20

Kudos for a correct solution.

Statement 1:
x could be 14
1, 14
2, 7
1+14+2+7=24

x could also be 15
1,15
3,5
1+15+3+5=24
Insufficient

Statement 2: 10 < x < 20
Again, x could be 14 or 15
Insufficent

Combined, 14 or 15 still does not give us a unique value

Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: What is the value of integer x?  [#permalink]

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1
Bunuel wrote:
What is the value of integer x?

(1) The sum of all the unique factors of x is 24.

(2) 10 < x < 20

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

E. On this Data Sufficiency problem, your best bet is to Play Devil's Advocate and try to find two values of x for which the conditions are met. For statement 1, that the sum of all unique factors of x is 24, the easiest number to pick is 23, as it's a prime number whose only other factor (than itself) is 1. 1 + 23 = 24, so you have one easy answer. Then you should start thinking whether there's a number lower than 23 (since any number higher will have at least 24 as one of its factors), and there you can use statement 2 as a hint. For statement 2 to be true, at least one number in that range must satisfy statement 1. And since no prime numbers will work (with only themselves and 1 as factors, none will reach a sum of 24) your options are:

12 (which has as factors 1, 2, 3, 4, 6, and 12 - the sum of which is greater than 24)

14 (which has as factors 1, 2, 7, and 14 - this one works as that sum is 24)

15 (which has as factors 1, 3, 5, and 15 - this one also works as that sum is 24)

And now you're done - with two different values for x that each satisfy both statements, the two statements together are not sufficient, and the answer is E.
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Intern  B
Joined: 06 Jun 2014
Posts: 11
Re: What is the value of integer x?  [#permalink]

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What about 11 + 13 ...Ans C .....am i wrong... pls clarify..
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8001
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the value of integer x?  [#permalink]

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1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the value of integer x?

(1) The sum of all the unique factors of x is 24.

(2) 10 < x < 20

In the original condition, there is 1 variable(x), which should match with the number of equations.
So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), x=14, 15, which is not unique and not sufficient.
For 2), x is not unique and not sufficient. When 1) & 2), x=14, 15, which is not unique and not sufficient. Therefore, the answer is E.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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GRE 1: Q169 V154 Re: What is the value of integer x?  [#permalink]

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Poor quality question i believe this one
I did get this right but i feel the question wants us to check for all the values between 10 and 20

Toooo much work..
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Intern  Joined: 20 Apr 2017
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Re: What is the value of integer x?  [#permalink]

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hi, the question is how do you know to pick 14,15? there are so many numbers between 11-19, how to complete this question within 2min? anyone could help?
Thanks!
vinoo7 wrote:
What about 11 + 13 ...Ans C .....am i wrong... pls clarify..
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Re: What is the value of integer x?  [#permalink]

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_________________ Re: What is the value of integer x?   [#permalink] 26 Jan 2019, 16:15
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