=If x and Y are integers and 2<x<y, does y =16
1) The GCF of x and y is 2
2) The lowest common multiple of x and y is 48
Veritas Quest-Dint get the explanation
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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]
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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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
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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Hi Rich,
Can we solve this question with the help of Algebra too!!
Thanks
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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Target question: Does y = 16?[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
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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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).
GMAT assassins aren't born, they're made,
Rich
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).
GMAT assassins aren't born, they're made,
Rich