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by theCodeToGMAT » Sat Oct 12, 2013 6:48 pm

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Is the Answer [spoiler]{C}[/spoiler]??

Given: y > x > 2

To find: y=16?

Statement 1:
x = 2 x a
y = 2 x b
a & b can be any values.
a=3, b=8 YES
a=3, b=5 NO
INSUFFICIENT


Statement 2:
48=2x2x2x2x3
Possible combinations can be
x = 4
y = 48 = NO
Or,
x = 3
y = 16 = YES
INSUFFICIENT

Combining..
x = 2 x 3 = 6
y = 2 x 2 x 2 x 2 = 16
[spoiler]{C}[/spoiler]
R A H U L
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by [email protected] » Sat Oct 12, 2013 8:11 pm

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Hi shibsriz,

Rahul's explanation is correct; by TESTing values, he's able to prove the correct answer is C.

There is one deduction that I will point out though (that is ultimately incorrect):

In the prompt, we're told Y > X > 2, so neither X nor Y can equal 2. In Fact 1, we're told that the GCF of the two numbers is 2. This means that X and Y are EVEN. However, it DOES NOT mean that X and Y can be "any even numbers". For the GCF to be 2, X and Y can't have any other factors in common besides 1 and 2.

The TESTed values (6 and 16, 6 and 10) both "fit" Fact 1 because they have a GCF of 2, not because they're both even. These details are exceptionally important in DS questions, in which a missed (or misunderstood) piece of information can be the different between the correct answer and one of the 4 incorrect ones.

GMAT assassins aren't born, they're made,
Rich
Last edited by [email protected] on Sun Oct 13, 2013 3:18 pm, edited 1 time in total.
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by [email protected] » Sat Oct 12, 2013 9:05 pm

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Hi Rich,

Can we solve this question with the help of Algebra too!!

Thanks
[email protected] wrote:Hi shibsriz,

Rahul's explanation is correct; by TESTing values, he's able to prove the correct answer is C.

There is one deduction that I will point out though (that is ultimately incorrect):

In the prompt, we're told Y > X > 2, so neither X nor Y can equal 2. In Fact 1, we're told that the GCF of the two numbers is 2. This means that by X and Y are EVEN. However, it DOES NOT mean that X and Y can be "any even numbers". For the GCF to be 2, X and Y can't have any other factors in common besides 1 and 2.

The TESTed values (6 and 16, 6 and 10) both "fit" Fact 1 because they have a GCF of 2, not because they're both even. These details are exceptionally important in DS questions, in which a missed (or misunderstood) piece of information can be the different between the correct answer and one of the 4 incorrect ones.

GMAT assassins aren't born, they're made,
Rich
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by Brent@GMATPrepNow » Sun Oct 13, 2013 7:57 am

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[email protected] wrote:If x and Y are integers and 2 < x < y, does y = 16?

1) The greatest common factor (GCF) of x and y is 2
2) The least common multiple (LCM) of x and y is 48
Target question: Does y = 16?

Statement 1: The greatest common factor (GCF) of x and y is 2
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 16, in which case y does equal 16
Case b: x = 2 and y = 4, in which case y does not equal 16
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT


Statement 2: The least common multiple (LCM) of x and y is 48
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 3 and y = 16, in which case y does equal 16
Case b: x = 12 and y = 48, in which case y does not equal 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Whenever we see a question involving GCF and LCM, we should recall the following rule:
(the GCF of x and y)(the LCM of x and y) = xy
Plug in statements to get: (2)(48) = xy
So, we know that xy = 96 AND we know that 2 < x < y
Start checking pairs of values (there aren't many) such that xy = 96 AND 2 < x < y:
x = 3 and y = 32 (does not satisfy statements 1 or 2)
x = 4 and y = 24 (does not satisfy statements 1 or 2)
x = 6 and y = 16 (YES, satisfies statements 1 and 2)
x = 8 and y = 12 (does not satisfy statements 1 or 2)

Now that we've checked all possible values for x and y, we can see that y must equal 16
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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by [email protected] » Sun Oct 13, 2013 3:22 pm

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Hi shibsriz,

If you're looking for a more "math-based" approach, then you could use prime factorization (Rahul essentially did that in his explanation). TESTing values is a remarkably useful approach on many Quant questions though, so you should look for opportunities to practice it (and use it on CATs).

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