prav04 wrote:
There are two types of rolls on a counter, plain rolls and seeded rolls. What is the total number of rolls on the counter?
(1) The ratio of the number of seeded rolls on the counter to the number of plain rolls on the counter Is 1 to 5.
(2) There are 16 more plain rolls than seeded rolls on the counter.
Given: There are two types of rolls on a counter, plain rolls and seeded rolls. Let P = # of plain rolls
Let S = # of seeded rolls
Target question: What is the value of P + S? Statement 1: The ratio of the number of seeded rolls on the counter to the number of plain rolls on the counter Is 1 to 5. In other words, S/P = 1/5
Cross multiply to get:
5S = PThere are several values of S and P that satisfy statement 1. Here are two:
Case a: S = 1 and P = 5. In this case, the answer to the target question is
S + P = 1 + 5 = 6Case b: S = 2 and P = 10. In this case, the answer to the target question is
S + P = 2 + 10 = 12Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: There are 16 more plain rolls than seeded rolls on the counter.In other words,
P = S + 15There are several values of S and P that satisfy statement 1. Here are two:
Case a: S = 1 and P = 16. In this case, the answer to the target question is
S + P = 1 + 16 = 17Case b: S = 2 and P = 17. In this case, the answer to the target question is
S + P = 2 + 17 = 19Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that
5S = PStatement 2 tells us that
P = S + 15ASIDE: Although we COULD solve the above system of equations (and then find the value of
P + S), we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.
Since we COULD answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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