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# The ratio of local and international calls made by Amy...

tagged by: AAPL

### Top Member

#### The ratio of local and international calls made by Amy...

The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21

The OA is D.

Local international ratio 5x/2x. Then local international ratio 5x/3x.

Can I say
$$\frac{5}{3}=\frac{5x}{2x+3}$$
and solve for x?

I don't have clear this PS question. I appreciate if any expert explains it to me. Thank you so much.

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
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Followed by:
1237 members
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GMAT Score:
770
AAPL wrote:
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21
Let L = number of local calls made this week
Let N = number of international calls made this week

The ratio of local and international calls made by Amy this week is 5 to 2
So, L/N = 5/2
Cross multiply to get: 2L = 5N

The ratio changes to 5 to 3 after Amy makes three more international calls
So, now N+3 = number of international calls made this week
And L still equals number of local calls made this week
We can write: L/(N + 3) = 5/3
Cross multiply to get: 3L = 5(N + 3)
Expand to get: 3L = 5N + 15

We know have the following system of equations
3L = 5N + 15
2L = 5N

SUBTRACT the bottom equation from the top equation to get: L = 15

Cheers,
Brent

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### GMAT/MBA Expert

Legendary Member
Joined
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Posted:
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GMAT Score:
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AAPL wrote:
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21

The OA is D.

Local international ratio 5x/2x. Then local international ratio 5x/3x.

Can I say
$$\frac{5}{3}=\frac{5x}{2x+3}$$
and solve for x?

I don't have clear this PS question. I appreciate if any expert explains it to me. Thank you so much.
You could also back-solve and use a little logic. First, we know that local calls must be a multiple of 5, so only B, C, and D are options.
Next, we can see quickly that B doesn't make sense - if there had been exactly 5 local calls and 2 international calls, if 3 more international calls had been made, the ratio would have been 5:5, not 5:3. B is out.

Now we just have to test one of the two remaining answer choices. If it works, it's our answer. If it doesn't, the other is our answer.
If there had been 10 local calls, then there'd have been 4 international calls. (10:4 = 5:2.) If there'd been 3 more international calls, the ratio would have been 10:7. We want 5:3. So C is out.

We're left with D

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### GMAT/MBA Expert

GMAT Instructor
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AAPL wrote:
The ratio of local and international calls made by Amy this week is 5 to 2. If the ratio changes to 5 to 3 after Amy makes three more international calls, how many local calls did Amy make this week?

A. 3
B. 5
C. 10
D. 15
E. 21
The ratio of local to international calls is 5x : 2x. Since after three more international calls are made, resulting in a new ratio of 5 to 3, we can create the equation:

5x/(2x + 3) = 5/3

15x = 5(2x + 3)

3x = 2x + 3

x = 3

So Amy made 5(3) = 15 local calls this week.

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Scott Woodbury-Stewart Founder and CEO

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