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greenwich: Master | Next Rank: 500 Posts; Posts: 110; Joined: Sun Jul 18, 2010 4:00 pm; Thanked: 1 times; Followed by:2 members

Scholarship

by greenwich » Mon Jun 09, 2014 5:02 pm

1. A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

A. 5
B. 6
C. 9
D. 10
E. 15

2. At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

A. 6 to 1
B. 3 to 2
C. 2 to 3
D. 1 to 5
E. 1 to 6

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Source: Beat The GMAT — Problem Solving | Mon Jun 09, 2014 5:02 pm

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by [email protected] » Mon Jun 09, 2014 8:03 pm

Hi greenwich,

When posting questions, its best to post 1 question per string. This will keep the focus on just 1 question at a time and minimize any back-and-forth confusion between posts that focus on just one of the questions.

As it stands, both questions are based on the same "ratio" concepts. Knowing how to answer one question will help you to answer the other.

Q1: There are 3 types of scholarships; I'm going to assign a variable to each type:

A = the number of $1250 scholarships
B = the number of $2500 scholarships
C = the number of $4000 scholarships

From the prompt, we're told that there were twice as many $2500 scholarships as $4000 scholarships. This ratio can be written as...

B:C
2:1

We're also told that the number of $1250 scholarships is three times the number of $2500 scholarships. This ratio can be written as...

A:B
3:1

So, we have...

A:B
3:1
...B:C
...2:1

Combining ratios, we get...

A:B:C
6:2:1

This means that the number of $1250 scholarships is some multiple of 6 and the number of $2500 scholarships is an equivalent multiple of 2.

We're told that the number of $1250 scholarships totaled $37500....

37,500/1250 = 30

There were 30 $1250 scholarships awarded. Using the final ratio, we can deduce that there were 10 $2500 scholarships and 5 $4000 scholarships.

Final Asnwer:A

GMAT assassins aren't born, they're made,
Rich

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by [email protected] » Mon Jun 09, 2014 8:21 pm

Hi greenwich,

For the second question, we can tackle it in a similar fashion to how we tackled the first.

2. At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

A. 6 to 1
B. 3 to 2
C. 2 to 3
D. 1 to 5
E. 1 to 6

First, I'll assign some variables...

E = number of English Majors
H = number of History Majors
M = number of Math majors

We have twice as many English majors as History majors. As a ratio, we have...

E:H
2:1

We also have three times as many English majors as Math majors. That ratio can be written as...

E:M
3:1

Before combining ratios, it's worth noting that the number of English majors has to be a multiple of 2 AND a multiple of 3; thus, it's a multiple of 6...Adjusting the two ratios accordingly, we have...

E:H
6:3

E:M
6:2

Now we can combine them...

E:H:M
6:3:2

The ratio of H:M is 3:2

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by GMATGuruNY » Mon Jun 09, 2014 8:46 pm

greenwich wrote:1. A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

A. 5
B. 6
C. 9
D. 10
E. 15

Work BACKWARDS.

A total of $37500 was awarded in $1250 scholarships.
Thus, the number $1250 scholarships = 37500/1250 = 30.

it awarded three times as many $1250 scholarships as $2500 scholarships
Since the number of $1250 scholarships = 30, the number of $2500 scholarships = 10.

The Committee awarded twice as many $2500 scholarships as $4000.
Since the number of $2500 scholarships = 10, the number of $4000 scholarships = 5.

The correct answer is A.

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

by GMATGuruNY » Mon Jun 09, 2014 8:51 pm

greenwich wrote:2. At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

A. 6 to 1
B. 3 to 2
C. 2 to 3
D. 1 to 5
E. 1 to 6

Since there are twice as many English majors as history major, E/H = 2/1.
Since there are 3 times as many English majors as math majors, E/M = 3/1.

The question stem asks for the value of H/M.
Ratios can be MULTIPLIED:
H/M = H/E * E/M.
In the equation above, the values in red CANCEL OUT.
Thus:
H/M = H/E * E/M = 1/2 * 3/1 = 3/2.

The correct answer is B.

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by Brent@GMATPrepNow » Mon Jun 09, 2014 8:54 pm

At a certain college there are twice as many English majors as History majors and three times as many English majors as Math's majors. What is the ratio of the number of history majors to the number of math's majors?
6:1
3:2
2:3
1:5
1:6

Goal: Find the value of H:M

Let's set this up:
There are twice as many English majors as History majors: E:H = 2:1
There are three times as many English majors as Math's majors: E:M = 3:1

Notice that the common "bond" here is E - it will connect the required H and M terms.

In order to use the E to connect the H and M terms, we must make the two E values equal by creating equivalent ratios.

E:H = 2:1
Multiply both terms by 3 to get E:H = 6:3
Important step: If E:H = 6:3, then H:E = 3:6

E:M = 3:1
Multiply both terms by 2 to get E:M = 6:2

Now that the two E terms are equal, we can combine the ratios to get: H:E:M = 3:6:2
This means that H:M = 3:2

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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greenwich: Master | Next Rank: 500 Posts; Posts: 110; Joined: Sun Jul 18, 2010 4:00 pm; Thanked: 1 times; Followed by:2 members

by greenwich » Tue Jun 10, 2014 6:51 pm

greenwich wrote:1. A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

A. 5
B. 6
C. 9
D. 10
E. 15

2. At a certain college there are twice as many English majors as history majors and three times as many English majors as mathematics majors. What is the ratio of the number of history majors to the number of mathematics majors?

A. 6 to 1
B. 3 to 2
C. 2 to 3
D. 1 to 5
E. 1 to 6

It seems that the wording of the above 2 questions is similar:

twice as many English majors as history majors: E=2H

twice as many $2500 scholarships as $4000: In this case, $4000 is x and $2500 is 2x

What am I missing here?

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by [email protected] » Tue Jun 10, 2014 8:44 pm

Hi greenwich,

The two statements ARE remarkably similar, but you have to remember what the translations actually "mean":

"Twice as many English majors as History majors"

E = NUMBER of english majors
H = NUMBER of history majors

E = 2H

"Twice as many $2500 scholarships as $4000 scholarships"

X = NUMBER of $2500 scholarships
Y = NUMBER of $4000 scholarships

X = 2Y

The prompts expect you to deal with each variable individually, so you should assign a unique letter to each. If and when the question asks you to do arithmetic with the variables, then you can "translate" and simplify.

For example, if the question asked for the TOTAL NUMBER of $2500 and $4000 scholarships, you could write...

X + Y

OR you could translate and simplify. Since X = 2Y, then

X + Y = 2Y + Y = 3Y

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Thu Mar 15, 2018 9:17 am

greenwich wrote:1. A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?

A. 5
B. 6
C. 9
D. 10
E. 15

We can let the number of $1250 scholarships = a, the number of $2500 scholarships = b, and the number of $4000 scholarships = c.

Since the committee awarded twice as many $2500 scholarships as $4000 scholarships:

b = 2c

Since it awarded three times as many $1250 scholarships as $2500 scholarships:

a = 3b

Since b = 2c, we see that a = 3(2c) = 6c.

Since a total of $37500 was awarded in $1250 scholarships:

1250a = 37,500

a = 30

Since a = 6c, we see that c = a/6 = 30/6 = 5.

Answer: A

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