the ratio of number of red pens to the number of blue pens in his shop is 5:8. there are 51 one more blue pens then red pens if the number of red pens increased by 25 find the new ratio of number of red pens to the number of Blue pens
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Step-by-step explanation:
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GMAT Club Forum Index Problem Solving (PS)
The ratio of blue pens to red pens is 5:7 : Problem Solving (PS)
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AaronPond
EXPERT'S
POST
Dec 22, 2017


00:00
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DIFFICULTY:
   25% (medium)
QUESTION STATS:
based on 41 sessions
86% (01:52) correct
14% (02:22) wrong
The ratio of blue pens to red pens is 5:7. When 3 blue pens are added to the group and 9 red pens are removed, the ratio of blue pens to red pens becomes 3:2. How many red pens are there after the changes?
(A) 3
(B) 5
(C) 9
(D) 12
(E) 18
Spoiler: OA
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Most Helpful Expert Reply
AaronPond
EXPERT'S
POST
Updated on: Aug 15, 2018
There are a handful of ways to solve this problem. Let's look at two of them.
Do the Dang Math
First, we could solve this with just the raw algebra. The question tells us that the original ratio of blue to red pens is 5: 7. Thus,  and  (where  is the scaling factor of the ratio.) We don't know what "" is yet, but thinking of the ratio in these terms allows us to quickly simplify down to one variable.
The problem then tells us that if we were to add 3 to  (in other words, ) and subtract 9 from  (in other words, ), the new ratio would be 3:2. Mathematically, it would look like this:

Cross-multiplying the fractions gives us:




Note how "3" is a possible answer. However, this is a classic trap of the GMAT: including the "right answer to the wrong question" as one of the answer choices. We were not asked to solve for the original scaling factor prior to the change, . (Incidentally, if we solve for the number of blue pens after the change, we arrive at 15, another trap answer!) Make sure you focus on the actual target of the question: the number of red pens after the change. Thus, we need . Plugging  into our equation gives us 12.
Hope its help you
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