If x and y are positive, is 3x > 7y?
(1) x > y + 4
(2) -5x < -14y
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GMAT Set 10 Q13
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GMATGuruNY
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Question stem, rephrased:Abhijit K wrote:If x and y are positive, is 3x > 7y?
(1) x > y + 4
(2) -5x < -14y
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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Brent@GMATPrepNow
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Target question: Is 3x > 7y?Abhijit K wrote:If x and y are positive, is 3x > 7y?
(1) x > y + 4
(2) -5x < -14y
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
Cheers,
Brent
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Uva@90
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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.
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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GMATGuruNY
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Nice work!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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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Gurpreet singh
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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
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
