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GMAT Practice exam 2 - Rations

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Sat Jun 04, 2016 1:50 am

Hello BTG

Would appreciate a little help to the fastest approach to this ratio-question:

Thanks in advance

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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 » Sat Jun 04, 2016 2:24 am

The number of stamps that Kaye and Alberto had were in the ratio 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

20
30
40
60
900

The answer choices imply that the values in the problem are all MULTIPLES OF 10.

Since K:A = 5:3, the following options are implied:
K=50, A=30
K=100, A=60
K=150, A=90
K=200, A=120.

After K gives away 10 stamps and A receives 10 stamps, the resulting values for K and A must be in a ratio of 7 to 5:
K=40, A=40
K=90, A=70
K=140, A=100.
We can stop here, since 140:100 = 14:10 = 7:5.

Thus, after the exchange, K-A = 140-100 = 40.

The correct answer is C.

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lucas211: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Mon Aug 04, 2014 5:39 pmFollowed by: 2 members; Thanked: 1 times

by lucas211 » Sat Jun 04, 2016 2:49 am

GMATGuruNY wrote:
The number of stamps that Kaye and Alberto had were in the ratio 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

20
30
40
60
900
The answer choices imply that the values in the problem are all MULTIPLES OF 10.

Since K:A = 5:3, the following options are implied:
K=50, A=30
K=100, A=60
K=150, A=90
K=200, A=120.

After K gives away 10 stamps and A receives 10 stamps, the resulting values for K and A must be in a ratio of 7 to 5:
K=40, A=40
K=90, A=70
K=140, A=100.
We can stop here, since 140:100 = 14:10 = 7:5.

Thus, after the exchange, K-A = 140-100 = 40.

The correct answer is C.

Hi GMATGuru

Thanks for you reply.
I think I am missing the point; how do the answer choices imply that the values in the problem are all multiples of 10?

Thanks again

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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 » Sat Jun 04, 2016 3:00 am

lucas211 wrote: Hi GMATGuru

Thanks for you reply.
I think I am missing the point; how do the answer choices imply that the values in the problem are all multiples of 10?

Thanks again

Since all of the answer choices are multiples of 10, the values in the problem are also probably multiples of 10.

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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 » Sat Jun 04, 2016 8:50 am

The number of stamps that Kaye and Alberto had were in the ratio 5 : 3, respectively. After Kaye gave Alberto 10 of her stamps,the ratio of the number Kaye had to the number Alberto had was 7 : 5. As a result of this gift, Kaye had how many more stamps than Alberto?
A. 20
B. 30
C. 40
D. 6O
E. 9O

Another option is to solve the question using TWO 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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rsarashi: Master | Next Rank: 500 Posts; Posts: 186; Joined: Sat Dec 24, 2016 12:38 amFollowed by: 3 members; Thanked: 5 times

by rsarashi » Thu Sep 21, 2017 9:26 am

Hello Experts ,

I got my two equations like below.

K/A = 5/3
&
K-10/A+10 = 7/5

If i solve this i get the difference of 60

Please let me know where i am getting wrong.

Thanks.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Sep 21, 2017 7:37 pm

Hi rsarashi,

Although you did not show your work, I assume that you calculated the K = 150 and A = 90. While you are correct that the difference in those two numbers is 60, the question asks for the difference AFTER Kaye has given Alberto 10 stamps. After the gift, Kaye would have 140 stamps and Alberto would have 100 stamps.

Final Answer: [spoiler]40; C[/spoiler]

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Contact Rich at [email protected]

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pannalal: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Sep 20, 2017 5:42 pm; Thanked: 2 times

by pannalal » Thu Sep 21, 2017 9:06 pm

Given that the ratio of stamps between Kaye and Alberto is 5:3.
Assuming Kaye has 5x and Alberto has 3x stamps. When Kaye gives 10 of her stamps to Alberto, the ratio becomes 7:5.

Thus, (5x-10)/(3x+10) = 7/5
or 25x - 50 = 21x + 70
or 4x = 120
or x = 30.

Kaye has stamps = 5x - 10 = 140
Alberto has stamps = 3x + 10 = 100

Kaye has more stamps than Alberto = 140-100 = 40 stamps.

Answer: C

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Sep 25, 2017 3:30 pm

The number of stamps that Kaye and Alberto had were in the ratio 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

20
30
40
60
900

We are given that the number of stamps that Kaye and Alberto had was in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information, we can create the following equation:

(5x - 10)/(3x + 10) = 7/5

5(5x - 10) = 7(3x + 10)

25x - 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) - 10 = 140 stamps and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 - 100 = 40 more stamps than Alberto has.

Answer: C

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[email protected]

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