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A university awarded grants in the amount of either $7,000 or $10,000

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A university awarded grants in the amount of either $7,000 or $10,000 [#permalink]

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New post 26 Feb 2017, 09:48
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Difficulty:

  45% (medium)

Question Stats:

66% (01:00) correct 34% (01:47) wrong based on 44 sessions

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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.

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Re: A university awarded grants in the amount of either $7,000 or $10,000 [#permalink]

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New post 11 Sep 2017, 02:03
1
Let no. of $7,000 grants =a
No. of $10,000 grants =b
$7,000a + $10,000b = $2,300,000
=>7a + 10b = 2300

Find if a>b ?

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

so a+b = 275
We got 2 equations on a and b so we can find values of a and b and compare. Sufficient
equations:
a+b =275
7a + 10b = 2300

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

10000b = 200000 +7000a
=> 10b =200 +7a
We got 2 equations on a and b so we can find values of a and b and compare. Sufficient
equations:
10b =200 +7a
7a + 10b = 2300

Answer: D
Re: A university awarded grants in the amount of either $7,000 or $10,000   [#permalink] 11 Sep 2017, 02:03
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A university awarded grants in the amount of either $7,000 or $10,000

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