A, B and C share $315 in such a way that for every $2 that A gets, B g

Question

A, B and C share $315 in such a way that for every $2 that A gets, B gets $5 and for every $4 that B gets, C gets $7. How much does C get?

A. 100
B. 125
C. 150
D. 175
E. 200

Abhishek009 · Answer

A : B = 2 : 5 
 B : C = 4 : 7

So,  A : B : C = 8 : 20 : 35

Hence, C gets  \frac{315}{(8+20+35)}*35 = 175 , Answer must be (D)

abannore · Answer

Answer: D

Suppose A gets x coins of $2 each. For every $2 that A gets, B gets $5. So B also gets x coins of $5.
Amount with A = $2x
Amount with B = $5x

Now out of these $5x amount, we need to find number of coins that will amount to $4.
So for $ \frac{(5x)}{4} , C gets $7.

Amount with C =  \frac{(5x)*7}{4} 
Total amount = 315

2x+5x+ \frac{(5x*7)}{4}  = 315
x=20

Amount C gets =  \frac{(5*20)}{4} *7 = $175

GMATCheater · Answer

Alternative Approach (Works only with these answer choices):
The problem tells us that C gets $7 for a certain amount B gets. This means that the total amount C gets has to be some multiple of 7. 175$ is the only multiple of 7 in the answer choices and therefore D is the answer.

ScottTargetTestPrep · Answer

Solution:

We can create the equations:

A + B + C = 315

And

A/B = 2/5

5A = 2B

A = 2B/5

And

B/C = 4/7

4C = 7B

C = 7B/4

Substituting, we have:

2B/5 + B + 7B/4 = 315

Multiplying by 20, we have:

8B + 20B + 35B = 6,300

63B = 6,300

B = 100

So C = 7(100)/4 = 175.

Alternate Solution:

Let’s create a 3-way ratio of A : B : C.

Let’s first set up A : B as 2 : 5 and B : C as 4 : 7. Now, we can’t combine them “as is” because the B numbers don’t match. However, we see that if we convert each ratio such that the B number is LCM(5,4) = 20, then the 3-way ratio can be completed.

Multiplying the ratio 2 : 5 by 4, we get the equivalent ratio of A: B as 8 : 20. Similarly, if we multiply the ratio 4 : 7 by 5, we obtain B : C as 20 : 35. The B numbers are in agreement; in both ratios, the B number is now 20, and so a 3-way ratio can be created.

Thus, the A : B : C ratio can be expressed as 8 : 20 : 35, or 8x : 20x : 35x.

We now have:

8x + 20x + 35x = 315

63x = 315

x = 5

Thus, C gets 35 x 5 = $175.

Answer: D

A, B and C share $315 in such a way that for every $2 that A gets, B g

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GMAT Problem Solving (PS) Questions

A, B and C share $315 in such a way that for every $2 that A gets, B g

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