Fractions/Ratios

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Fractions/Ratios

by piyush2694 » Fri Dec 21, 2018 12:34 am

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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.

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by Brent@GMATPrepNow » Fri Dec 21, 2018 7:06 am

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piyush2694 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 = P
There 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 = 6
Case b: S = 2 and P = 10. In this case, the answer to the target question is S + P = 2 + 10 = 12
Since 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 + 15
There 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 = 17
Case b: S = 2 and P = 17. In this case, the answer to the target question is S + P = 2 + 17 = 19
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 5S = P
Statement 2 tells us that P = S + 15
ASIDE: 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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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