Is p q (1) 2p/3

Question

Is  p > q  ?

(1)  \frac{2p}{3} < \frac{3q}{8}

(2)  \frac{7p}{11} < \frac{4q}{5}

GMATGuruNY · Accepted Answer

Statement 1: \frac{2}{3}p < \frac{3}{8}q Multiplying by the LCM of the two denominators -- 24 -- we get: 16p < 9q p < \frac{9}{16}q Case 1: q=1, implying that p < 9/16 If p=0, then pq, so the answer to the question stem is YES. INSUFFICIENT. Statement 2: \frac{7}{11}p < \frac{4}{5}q Multiplying by the LCM of the two denominators -- 55 -- we get: 35p < 44q p < \frac{44}{35}q Case 1: q=1, implying that p < 44/35 If p=0, then pq, so the answer to the question stem is YES. INSUFFICIENT. Statements combined: 16p < 9q --> difference between the coefficients = 16-9 = 7 35p < 44q --> difference between the coefficients = 44-35 = 9 To combine the two inequalities so that p and q are ISOLATED, the difference between the coefficients must be THE SAME in each inequality. The LCM of the two differences in blue is 63. To yield a difference of 63 in each inequality, multiply the first by 9 and the second by 7: 9*16p < 9*9q --> 144p < 81q --> difference between the coefficients = 144-81 = 63 7*35p < 7*44q --> 245p < 308q --> difference between the coefficients = 308-245 = 63 Adding together the resulting inequalities in green, we get: 144p + 245p < 81q + 308q 389p < 389q p < q Thus, the answer to the question stem is NO. SUFFICIENT. C

chetan2u · Answer

91% have answered wrongly, so I would agree it is a tough one.

If short of time,
a) p and q could be negative or positive, so both the statements are not sufficient on their own.
b) So, answer could be C or E. 
c) As we have two ranges in two statements, chances of getting C as answer is more.

Solution :-

1.  \frac{2p}{3} < \frac{3q}{8} 
 p<\frac{9q}{16} 
If q is positive...... p<\frac{9q}{16}<q ...YES
If q is negative and say q=-16 and p=-17..... p<q<\frac{9q}{16} ..YES
If q is negative and say q=-16 and p=-15..... q<p<\frac{9q}{16} ..NO
Insuff

2. 7p/11 < 4q/5
 p<\frac{44q}{35} 
If q is negative...... p<\frac{44q}{35}<q ...YES
If q is positive and say q=35 and p=14..... p<q<\frac{44q}{35} ..YES
If q is negative and say q=35 and p=42..... q<p<\frac{44q}{35} ..NO
Insuff

Combined..
If q is positive, the combined range from the two statements tells us that p<q.
Similarly combined range from the two statements tells us that p<q when q is negative.
Hence p<q is always true.

C

Archit3110 · Answer

target determine whether p>q #1 2p/3 < 3q/8 can be written as 16p-9q/24<0 possible at p,q; (1,2) ; ( -1,-1) insufficient #2 7p/11 < 4q/5 can be written as 35p-44q/55<0 possible at p,q; ( 1,1) ; ( -1,0) ; (1,2) insufficient from 1&2 we can say that q>p then both #1 & #2 would be valid OPTION C

gmatophobia · Answer

Hello  GMATGuruNY

When you combined the inequalities why didn't you just add the inequalities the way they are -

From Statement 1 we know

16p < 9q

From Statement 2 we know

35p < 44q

Can we not add the above two expressions to get -

51p < 53q

Posted from my mobile device

GMATGuruNY · Answer

In S1, the coefficient for p is GREATER than that for q.
As a result, we cannot determine whether p > q.
In S2, the coefficient for p is LESS than that for q.
As a result, we cannot determine whether p > q.

Is p > q?

The answer will be a definite NO if we can combine the two inequalities so that p and q have the SAME coefficient.
Simply adding the two inequalities does not accomplish this goal.
The approach in my earlier post yields the same coefficient for p and q, allowing us to prove that p < q and answer the question stem with a definite NO.

Bunuel · Answer

Is p > q ? (1) \frac{2p}{3} < \frac{3q}{8} Cross-multiply to get 16p < 9q. Now, inequalities of a form ax < by, if no constraints are given on x and y , are NEVER sufficient to answer whether x > y. Not sufficient. (2) \frac{7p}{11} < \frac{4q}{5} Cross-multiply to get 35p < 44q. As discussed above, this cannot be sufficient to determine whether x > y. Not sufficient. (1)+(2) We are given two inequalities: 16p < 9q and 35p <44q Multiplying the first inequality by 35 and the second inequality by 16, to equate the coefficients of p in both, we get (don't actually do the math): 35*16p < 35*9q 16*35p < 16*44q Subtract the first one from the second: 0 < q(16*44 - 35*9) 0 < q(positive) q > 0 Multiply the first inequality by 44 and the second inequality by 9, to equate the coefficients of q in both, we get (don't actually do the math): 44*16p < 44*9q 9*35p < 9*44q Subtract the second one from the first: p (44*16 - 9*35) < 0 p(positive) < 0 p < 0 Therefore, q, which is positive, is greater than p, which is negative, giving a NO answer to the question whether p > q. Sufficient. Answer: C.

Is p > q (1) 2p/3 < 3q/8 (2) 7p/11 < 4q/5

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