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Updated on: 14 Jan 2020, 23:06
Originally posted by rajthakkar on 20 Feb 2015, 01:41.
Last edited by Bunuel on 14 Jan 2020, 23:06, edited 1 time in total.
Last edited by Bunuel on 14 Jan 2020, 23:06, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
60% (02:19) correct
40%
(01:59)
wrong
based on 78
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Not Attempted Yet
If p and q are non-negative, is p + q > pq ?
(1) p = q
(2) p + q > p^2 + q^2
(1) p = q
(2) p + q > p^2 + q^2
20 Feb 2015, 13:05
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Hi rajthakkar,
This question is perfect for TESTing VALUES (and knowing a few specific Number Properties would likely help).
**NOTE: I'm going to assume that this question has just 2 variables: P and Q; any difference in capitalization/lower-case in the original prompt is an oversight**
We're told that P and Q are NON-NEGATIVE. We're asked if P+Q > (P)(Q). This is a YES/NO question.
Fact 1: P = Q
IF...
P=Q=0
Then 0+0 is NOT > (0)(0) and the answer to the question is NO.
IF....
P=Q=1
Then 1+1 IS > (1)(1) and the answer to the question is YES.
Fact 1 is INSUFFICIENT.
Fact 2: P + Q > P^2 + Q^2
In this Fact, while one of the variables COULD be 0, they CANNOT BOTH be 0. This means that one or both of the variables must be POSITIVE (but they both have to be relatively SMALL, they CAN'T BOTH be 1 and they CAN'T BOTH be greater than 1, otherwise the inequality won't hold true).
At this point, you might recognize some Number Properties or you might want to prove your ideas by TESTing VALUES. Here, one or both of the numbers will be a fraction. The Number Property in question is that since one (or both) are positive fractions, P+Q will always be > than (P)(Q), since multiplying a positive by a fraction makes the product SMALLER.
IF...
P = 1/2
Q = 0
Then 1/2 + 0 IS > (1/2)(0) and the answer to the question is YES.
IF...
P = 1
Q = 1/2
Then 1 + 1/2 IS > (1)(1/2) and the answer to the question is YES.
IF...
P = 1.1
Q = 1/2
Then 1.1 + 1/2 IS > (1.1)(1/2) and the answer to the question is YES.
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This question is perfect for TESTing VALUES (and knowing a few specific Number Properties would likely help).
**NOTE: I'm going to assume that this question has just 2 variables: P and Q; any difference in capitalization/lower-case in the original prompt is an oversight**
We're told that P and Q are NON-NEGATIVE. We're asked if P+Q > (P)(Q). This is a YES/NO question.
Fact 1: P = Q
IF...
P=Q=0
Then 0+0 is NOT > (0)(0) and the answer to the question is NO.
IF....
P=Q=1
Then 1+1 IS > (1)(1) and the answer to the question is YES.
Fact 1 is INSUFFICIENT.
Fact 2: P + Q > P^2 + Q^2
In this Fact, while one of the variables COULD be 0, they CANNOT BOTH be 0. This means that one or both of the variables must be POSITIVE (but they both have to be relatively SMALL, they CAN'T BOTH be 1 and they CAN'T BOTH be greater than 1, otherwise the inequality won't hold true).
At this point, you might recognize some Number Properties or you might want to prove your ideas by TESTing VALUES. Here, one or both of the numbers will be a fraction. The Number Property in question is that since one (or both) are positive fractions, P+Q will always be > than (P)(Q), since multiplying a positive by a fraction makes the product SMALLER.
IF...
P = 1/2
Q = 0
Then 1/2 + 0 IS > (1/2)(0) and the answer to the question is YES.
IF...
P = 1
Q = 1/2
Then 1 + 1/2 IS > (1)(1/2) and the answer to the question is YES.
IF...
P = 1.1
Q = 1/2
Then 1.1 + 1/2 IS > (1.1)(1/2) and the answer to the question is YES.
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
14 Jan 2020, 02:44
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P and Q are NON-NEGATIVES. Hence P and Q can be zero or positive numbers.
And we're asked if P+Q > (P)(Q)?
Statement 1:
P = Q
1) IF P=Q=0
Then 0+0 is NOT > (0)(0) and the answer to the question is NO.
2) IF P=Q=1
Then 1+1 IS > (1)(1) and the answer to the question is YES.
ONE NO AND ONE YES OR STATEMENT 1 is INSUFFICIENT.
Cancel AD.
Statement 2: P + Q > P^2 + Q^2
1) IF P = 1/2, Q = 0 which satisfies Statement 2,
Then 1/2 + 0 IS > (1/2)(0) and the answer to the question is YES.
2) IF P = 1, Q = 1/2 which satisfies Statement 2,
Then 1 + 1/2 IS > (1)(1/2) and the answer to the question is YES.
Hence Statement 2 is SUFFICIENT or
Choose answer option B.
And we're asked if P+Q > (P)(Q)?
Statement 1:
P = Q
1) IF P=Q=0
Then 0+0 is NOT > (0)(0) and the answer to the question is NO.
2) IF P=Q=1
Then 1+1 IS > (1)(1) and the answer to the question is YES.
ONE NO AND ONE YES OR STATEMENT 1 is INSUFFICIENT.
Cancel AD.
Statement 2: P + Q > P^2 + Q^2
1) IF P = 1/2, Q = 0 which satisfies Statement 2,
Then 1/2 + 0 IS > (1/2)(0) and the answer to the question is YES.
2) IF P = 1, Q = 1/2 which satisfies Statement 2,
Then 1 + 1/2 IS > (1)(1/2) and the answer to the question is YES.
Hence Statement 2 is SUFFICIENT or
Choose answer option B.
