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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Feb 24, 2015 3:36 am
Abhijit K wrote:If x and y are positive, is 3x > 7y?

(1) x > y + 4

(2) -5x < -14y
Question stem, rephrased:
Is x > (7/3)y?

Statement 1: x > y+4
Case 1: y=1, x=6
Plugging x=6 and y=1 into x>(7/3)y, we get:
6 > 7/3.
YES.

Case 2: y=6, x=11
Plugging x=11 and y=6 into x>(7/3)y, we get:
11 > 14.
NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2: -5x < -14y
Dividing each side by -5, we get:
x > (14/5)y.
Since 14/5 > 7/3 and y is positive, (14/5)y > (7/3)y.
Linking together x > (14/5)y and (14/5)y > (7/3)y, we get:
x > (14/5)y > (7/3)y
x > (7/3)y.
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Tue Feb 24, 2015 10:07 am
Abhijit K wrote:If x and y are positive, is 3x > 7y?

(1) x > y + 4
(2) -5x < -14y
Target question: Is 3x > 7y?

Given: x and y are positive

Statement 1: x > y + 4
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 6 and y = 1 (this satisfies the condition that X > y + 4). In this case 3x is GREATER THAN 7y
Case b: x = 10 and y = 5 (this satisfies the condition that X > y + 4). In this case 3x is LESS THAN 7y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: -5x < -14y
Divide both sides by -1 to get 5x > 14y
NOTE: we need to compare 3x and 7y. So, let's fiddle with the inequality 5x > 14y
Divide both sides by 2 to get 2.5x > 7y

IMPORTANT: If x is positive (which we're told it is), then 3x > 2.5x. So, let's add this to our inequality to get...
3x > 2.5x > 7y
From this, we can conclude that it MUST be the case that 3x > 7x
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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Brent
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by Uva@90 » Tue Feb 24, 2015 7:26 pm
Hi Mitch/Brent,

Could you please advise me whether my below approach for the Statement-2 is correct or not.

Question Stem is 3x > 7y ? (Yes/No Question)

Stmt-2: -5x < -14y

Divide by -1 ==> 5x > 14y

Multiply question stem by 2 ==> 6x > 14y

Since X and Y are positive and stmt 2 says 5x > 14y . So, 6x will always be greater than 14y.
Hence sufficient.

is this correct one ?

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Uva.
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by GMATGuruNY » Tue Feb 24, 2015 7:43 pm
Uva@90 wrote:Hi Mitch/Brent,

Could you please advise me whether my below approach for the Statement-2 is correct or not.

Question Stem is 3x > 7y ? (Yes/No Question)

Stmt-2: -5x < -14y

Divide by -1 ==> 5x > 14y

Multiply question stem by 2 ==> 6x > 14y

Since X and Y are positive and stmt 2 says 5x > 14y . So, 6x will always be greater than 14y.
Hence sufficient.

is this correct one ?

Regards,
Uva.
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by ApolloYR » Thu Nov 19, 2015 6:07 am
Hi guys,

In the steam we are told "x and y are positive", but we are not told if x and y are integers.

When should you consider the none integer numbers?

Thanks
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by Gurpreet singh » Sun May 22, 2016 7:11 am
I solved it in a different way not sure if it is the right approach or the inference is correct.

question stem
is 3x>7y or 3x-7y>0

st 1
x>y+4 or x-y>4
lets plugin in some values
x=6 & y=1(diff has to be >4)
18-7>4
x=10 & y=5
30-35=-5<0
statement is not sufficient.

Statement 2
-5x<-14y
-5x+14y<0
5x-14y>0

In above we can only put in values which should ensure the diff is greater then 0

Hence x=3 and y=1

putting the values in the question stem

9-7=2>0
sufficient
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