Stamps

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paresh_patil: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Thu Jan 03, 2013 10:30 pm; Thanked: 4 times

by paresh_patil » Fri Mar 15, 2013 1:13 am

The number of stamps that K and A had were in the ratio 5:3, respectively. After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5. As a result of this gift, K had how many more stamps than A?
A) 20
B) 30
C) 40
D) 60
E) 90

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Source: Beat The GMAT — Problem Solving | Fri Mar 15, 2013 1:13 am

neha24: Senior | Next Rank: 100 Posts; Posts: 72; Joined: Fri Mar 01, 2013 8:45 amFollowed by: 4 members; Thanked: 12 times

by neha24 » Fri Mar 15, 2013 1:27 am

my take C
k had 5x
a had 3x
now 5x-10 : 3x +10 :: 7:5
this means X =30
hence new difference =40

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Fri Mar 15, 2013 1:29 am

Let us assume that now Kaye has 7x stamps and Alberto has 5x stamps.
Hence, Kaye has 2x stamps more than Alberto.

Before the gift, Kaye had (7x + 10) stamps and Alberto had (5x - 10) stamps.
So, (7x + 10)/(5x - 10) = 5/3
--> 3(7x + 10) = 5(5x - 10)
--> (21x + 30) = (25x - 50)
--> 4x = 80
--> 2x = 40

The correct answer is C.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Mar 15, 2013 4:52 am

paresh_patil wrote:The number of stamps that K and A had were in the ratio 5:3, respectively. After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5. As a result of this gift, K had how many more stamps than A?
A) 20
B) 30
C) 40
D) 60
E) 90

We can plug in the answers, which represent K-A after the exchange.

Answer choice C: after the exchange, K-A = 40
Since K:A = 7:5 and K-A = 40, we get:
K:A = 7:5 = 70:50 = 140:100, with the result that K-A = 140-100 = 40.

Before K gave away 10 stamps, K had 10 MORE stamps, while A had 10 FEWER stamps.
Thus:
K = 140+10 = 150 and A = 100-10 = 90, with the result that K:A = 150:90 = 5:3.
Success!

The correct answer is C.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Mar 15, 2013 7:03 am

paresh_patil wrote:The number of stamps that K and A had were in the ratio 5:3, respectively. After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5. As a result of this gift, K had how many more stamps than A?
A) 20
B) 30
C) 40
D) 60
E) 90

We can also solve the question using 2 variables.
Let K = # of stamps K had after the exchange
Let A = # of stamps A had after the exchange
This means that K+10 = # of stamps K had before the exchange
This means that A-10 = # of stamps A had before the exchange

Note: Our goal is to find the value of K-A

The number of stamps that K and A (originally) had were in the ratio 5:3
So, (K+10)/(A-10) = 5/3
We want a prettier equation, so let's cross multiply to get 3(K+10) = 5(A-10)
Expand: 3K + 30 = 5A - 50
Rearrange: 3K - 5A = -80

After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5
So, K/A = 7/5
We want a prettier equation, so let's cross multiply to get 5K = 7A
Rearrange to get: 5K - 7A = 0

At this point we have two equations:
5K - 7A = 0
3K - 5A = -80

Our goal is to find the value of K - A.
IMPORTANT: We need not solve for the individual values of K and A. This is great, because something nice happens when we subtract the blue equation from the red equation.
We get: 2K - 2A = 80
Now divide both sides by 2 to get: K - A = 40

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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