rajlal wrote:
At noon of a certain day, when 5 pens and 3 pencils were placed in a drawer, the ratio of the number of pens to the number of pencils in that drawer became 47 to 17.
Quantity A |
Quantity B |
The ratio of the number of pens to the number of pencils in the drawer immediately before noon of that day |
\(\frac{3}{1}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Can someone explain this in very very simpler terms?
KEY INFORMATION: After the pens and pencils were added, the ratio of the number of pens to the number of pencils in that drawer became 47 to 17 (aka 47/17).
Here's one possible scenario:
BEFORE NOON, the drawer contained 42 pens and 14 pencils.
So, after the 5 pens and 3 pencils were added, the drawer contained 47 pens and 17 pencils, giving us our ratio of 47/17
In this case, ratio of the number of pens to the number of pencils in the drawer BEFORE NOON = 42/14 = 3/1
We get:
Quantity A: 3/1
Quantity B: 3/1
The two quantities are EQUAL
IMPORTANT: Are there any other scenarios that satisfy the given conditions?
YES! There are infinitely many scenarios, because the key ratio in the question (47/17) has INFINITELY MANY equivalent ration.
For example, 47/17 = 94/34 = 141/51 = 470/170 etcSo, let's examine another possible scenario
BEFORE NOON, the drawer contained 89 pens and 31 pencils.
So, after the 5 pens and 3 pencils were added, the drawer contained 94 pens and 34 pencils, giving us our ratio of 94/34, which is EQUIVALENT to 47/17
In this case, ratio of the number of pens to the number of pencils in the drawer BEFORE NOON = 89/31
We get:
Quantity A: 89/31
Quantity B: 3/1
The two quantities are NOT equal
Answer: D
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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