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A university awarded grants in the amount of either $7,000

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A university awarded grants in the amount of either $7,000

by BTGmoderatorLU » Mon Nov 04, 2019 3:13 am
Source: Princeton Review

A university awarded grants in the amount of either $7,000 or $10,000 to some incoming freshmen. The total amount of all such awards was $2,300,000. Did the university award more $7,000 grants than $10,000 grants to its incoming freshmen?

1) A total of 275 freshmen received grants in one of the two amounts.
2) The amount of money awarded in $10,000 grants was $200,000 more than the amount of money awarded in $7,000 grants.

The OA is D
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Nov 10, 2019 11:11 pm
BTGmoderatorLU wrote:Source: Princeton Review

A university awarded grants in the amount of either $7,000 or $10,000 to some incoming freshmen. The total amount of all such awards was $2,300,000. Did the university award more $7,000 grants than $10,000 grants to its incoming freshmen?

1) A total of 275 freshmen received grants in one of the two amounts.
2) The amount of money awarded in $10,000 grants was $200,000 more than the amount of money awarded in $7,000 grants.

The OA is D
Say there are x no. of $7,000 and y no. of $10,000 grants.

Thus, we have 7,000x + 10,000y = 230,000

7x + 10y = 230

We have to determine whether x > y.

Let's take each statement one by one.

1) A total of 275 freshmen received grants in one of the two amounts.

x + y = 275

We know that 7x + 10y = 230 and x + y = 275; we get the unique value of x and y. Sufficient

This is a DS question and not a PS, so we only need to be satisfied whether we get the unique values.

2) The amount of money awarded in $10,000 grants was $200,000 more than the amount of money awarded in $7,000 grants.

10,000y - 7,000x = 200,00
10y - 7x = 200

Again with the help of 7x + 10y = 230 and 10y - 7x = 200; we get the unique value of x and y. Sufficient

The correct answer: D

Hope this helps!

-Jay
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