IMO - B
Statement 1
Take x= 11 , y=6
x> y+4
However it does not satisfy x> (7/3)y
Take x= 1000 , y=1
x> y+4 And the condition x> (7/3)y is satisfied
Hence statement 1 is not sufficient
Statement 2
-5x < -14y
Mutiplying both sides by -1 , the sign of the eqn also changes
we get 5x > 14y
x> (14/5)y
Hence x> (7/3)y , the main condition is satisfied.
Hence B
3x
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Source: Beat The GMAT — Data Sufficiency |
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raghavsarathy
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mehravikas
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Answer should be - B
Statement 1 -
x = 10, y = 4
10 > 5 + 4 but 10 < 2.33 * 5
x = 6, y = 1
6 > 1 + 4 and 6 > 2.33 * 1
Insufficient
Statement 2 -
-5x < - 14y = multiply by -1
5x > 14y -> x > 14/5 * y
x > 2.8y therefore x will always be greater than 2.33 y
Statement 1 -
x = 10, y = 4
10 > 5 + 4 but 10 < 2.33 * 5
x = 6, y = 1
6 > 1 + 4 and 6 > 2.33 * 1
Insufficient
Statement 2 -
-5x < - 14y = multiply by -1
5x > 14y -> x > 14/5 * y
x > 2.8y therefore x will always be greater than 2.33 y
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Ian Stewart
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Looking only at S2, we have:
-5x < -14y
5x > 14y
3x > (3/5)*14y
3x > 8.4y
So we know that 3x > 8.4y, and we want to know if 3x > 7y. If y is positive, the answer is certainly 'yes', because then 8.4y > 7y. However, if y is negative, 8.4y is less than 7y. We might have:
y = -1
x = -2.5
Then 3x = -7.5 is certainly greater than 8.4y = -8.4, but 3x is not greater than 7y = -7. Statement 2 is not sufficient.
-5x < -14y
5x > 14y
3x > (3/5)*14y
3x > 8.4y
So we know that 3x > 8.4y, and we want to know if 3x > 7y. If y is positive, the answer is certainly 'yes', because then 8.4y > 7y. However, if y is negative, 8.4y is less than 7y. We might have:
y = -1
x = -2.5
Then 3x = -7.5 is certainly greater than 8.4y = -8.4, but 3x is not greater than 7y = -7. Statement 2 is not sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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raghavsarathy
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Hi Ian. The main statement says that x and y are positive. In such a situation the ans would be B right ?Ian Stewart wrote:Looking only at S2, we have:
-5x < -14y
5x > 14y
3x > (3/5)*14y
3x > 8.4y
So we know that 3x > 8.4y, and we want to know if 3x > 7y. If y is positive, the answer is certainly 'yes', because then 8.4y > 7y. However, if y is negative, 8.4y is less than 7y. We might have:
y = -1
x = -2.5
Then 3x = -7.5 is certainly greater than 8.4y = -8.4, but 3x is not greater than 7y = -7. Statement 2 is not sufficient.
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Ian Stewart
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Good point! When I was writing up my answer, I think I was remembering a different question that didn't have that restriction. Yes, since:raghavsarathy wrote:
Hi Ian. The main statement says that x and y are positive. In such a situation the ans would be B right ?
8.4 > 7
then if y is positive, we can multiply on both sides by y without reversing the inequality to get:
8.4y > 7y
so if x > 8.4y, then x certainly must be greater than 7y. So to clarify my post above, if x and y are positive, S2 is certainly sufficient. If you remove that condition from the question, then S2 is not sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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