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15 Nov 2017, 11:03
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
83% (00:59) correct
17%
(01:08)
wrong
based on 300
sessions
History
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Not Attempted Yet
15 Nov 2017, 11:38
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pushpitkc
Target question: What is the value of p+q?
Statement 1: r - s = 5
No information about p or q
So, statement 1 is NOT SUFFICIENT
Statement 2: rp + rq - sp - sq = 20
We can factor the left side in parts
Factor r from first 2 terms to get: r(p + q) - sp - sq = 20
Factor -s from last 2 terms to get: r(p + q) - s(p + q) = 20
Since we have p + q in common in both parts, we can combine the terms
We get: (r - s)(p + q) = 20
------------------------------------
ASIDE: This last step is no different from simplifying the expression 8k - 3k to get: (8 - 3)k
To be more general: b(something) - c(something) to get: (b - c)(something)
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Now that we know that (r - s)(p + q) = 20, we can see that p+q can have many different values.
So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that r - s = 5
Statement 2 tells us that (r - s)(p + q) = 20
Replace (r - s) with 5 to get: (5)(p + q) = 20
So, IT MUST be the case that (p + q) = 4
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
15 Nov 2017, 11:41
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(1) r-s=5. Nothing about p and q. Insufficient.
(2) rp+rq-sp-sq = 20. Or r(p+q) - s(p+q) = 20 or
(r-s)(p+q) = 20. Here we have factorised the left hand side. But still we cant say anything about (p+q) unless we know something about (r-s). (Because multiple cases are possible). Insufficient.
Combining the two statements: Substituting r-s=5, we get 5 (p+q) = 20 or p+q = 4. Sufficient.
Hence C answer.
(2) rp+rq-sp-sq = 20. Or r(p+q) - s(p+q) = 20 or
(r-s)(p+q) = 20. Here we have factorised the left hand side. But still we cant say anything about (p+q) unless we know something about (r-s). (Because multiple cases are possible). Insufficient.
Combining the two statements: Substituting r-s=5, we get 5 (p+q) = 20 or p+q = 4. Sufficient.
Hence C answer.
