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

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by BTGmoderatorLU » Tue Dec 17, 2019 5:02 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 Gene@KaplanGMAT » Tue Dec 17, 2019 5:12 pm
Let's call the number $10,000 grants "B" (for Big grants), and the number of $7,000 grants "L" (for Little grants).
And 10,000B + 7,000L = $2,300,000
And the question wants to know if L > B (it's a Yes/No DS problem).

Statement (1) tells us there were 275 total awards so B + L = 275. Between this and the original equation above, we'd have 2 distinct equations and 2 variables. So we could actually solve for "L" and for "B" (doesn't mean we *should* since its DS, but we *could*) so statement (1) is SUFFICIENT.

Statement (2) tells us 10,000B = 200,000 + 7,000L. Again, between this and the original equation above, we'd have 2 distinct equations with 2 variables. So we'd be able to solve for both "L" and for "B". SUFFICIENT.

[For the record, if you did actually solve in either of these, L=150 and B=125, so there were more $7000 grants]
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by SampathKp » Wed Dec 18, 2019 3:47 am
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
let number of freshmen who received $7000 grant be X and number of freshmen who received 10,000 grant be Y

We have 7000X +10000Y = 2300000 . One equation with 2 variables X and Y. To solve this equation for both variables X and Y we need another equation with Variables X and Y.

From (1) , we have X+Y = 275. So combining with given equation 7000X+10000Y=2300000 we can solve for X and Y and answer X>Y or not. SO (1) is Sufficient
From (2) , we have 10000Y = 7000X+200000 . So combining with given equation 7000X+10000Y=2300000 we can solve for X and Y and answer X>Y or not. So (2) is Sufficient.

Answer is D. Each Statement alone is sufficient to answer the question.
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