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Source: Veritas Prep; Book 08
Chapter: 4
Topic: Data Sufficiency
Question: 14
Question: Page 89
Solution: Page 91
14. A street vendor sells only apples and pineapples, and all apples weigh 6.5 ounces, while all pineapples weigh 13 ounces. If she sells twice as many apples as pineapples, how many apples does she sell.
(1) She sells 8 more apples than pineapples.
(2) She sells an equal amount, by weight, of apples and pineapples.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient to answer the question asked
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Answer:
Item; Weight; Quantity
Apples; 6.5 ounces; a
Pineapples; 13.0 ounces; p
a = 2p
Statement 1: a = p + 8. From the question we know that a = 2p. Substituting, we get 2p=p+8; p=8; a=16. This provides one value. Hence sufficient. Based on this the answer choice B, C, E are eliminated.
Statement 2: 6.5a = 13p; a=2p. This is the same as equation in the question [a=2p]. Since the answer choice mirrors the question, it is sufficient. The answer choice is D based on the concept above.
I formed this concept on another Veritas Prep Question provided on page 41. The solution is provided on page 45. The question is a drill.
Is 2x=3y+z
(1) \(x-z=\frac{3y}{2}\)
Solving statement 1, it becomes 2x=According to the Veritas Prep Answer, whenever a statement exactly mirrors the question stem, it is sufficient.
Why is the Answer Choice A and not D ? Please explain.
Hi,
your statement 1 solution is perfectly fine
a = p + 8. From the question we know that a = 2p. Substituting, we get 2p=p+8; p=8; a=16.===>this is giving a definite values APPLES=16 and pineapples=8
statement 2:
6.5a = 13p; a=2p.
now here got A=2P...IN THIS A and P are variables.
you can take A=16 P=18
OR A=4 P=2...SIMILARLY MANY PAIRS CAN BE FORMED...hence the answer is not fixed...it is depending on the unknown variables A and P.
more to add...in statement 1 because of given condition that A=P+8....THIS IS ONE EQUATION
FROM QUESTION STEM WE HAVE A=2P.....THIS IS 2ND EQUATION....so we have to equation and 2 unknown.hence we can solve for a fixed value
for statement 2:
equal amount, by weight, of apples and pineapples==>this gives A=2P
FROMQUESTION STEM ===>WE HAVE A=2P......SEE HERE BOTH THE THINGS ARE GIVING SAME EQUATION N=BUT WE HAVE 2 UNKNOWN VARIABLES THAT IS WHY WE ARE UNABLE TO SOLVE BY THIS SECOND STATEMENT.
HENCE A
HOPE IT HELPS