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

Question

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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curiousPope · Answer

Is D the correct answer?

Bunuel · Answer

The OA will be automatically revealed on Tuesday 12th of March 2024 01:30:35 AM Pacific Time Zone. Meanwhile, you are welcome to post your rationale behind D.

Edoua · Answer

D also is the correct answer

X person who received 7.000
Y who received 10.000

7.000x + 10.000y = 2.300.000

1- x +y =275 sufficient

2- 10.000y = 20.000 + 7000x

Is there any mistake on this?

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poojaarora1818 · Answer

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.

Solution

Statement 1 tells us 275 total freshmen who received grants in one of the two amounts

Let's consider the no. of $7000 = x
                 the no. of $10,000 = 275-x
So, form an equation

7000x + 10000(275-x)      = 2300000
7000x + 2750000-10000x = 2300000
-3000x                            = -450000
                          x          = -450000/-3000 =150
Now, we know 7000*150= 1050000 and 10000(275-150)= 1250000
We know $1250000 > $1050000 So, the answer is No
 Statement 1 is sufficient

Statement 2

Let's consider No. of $7000= x
                No. of $10,000 = y

We already know from the ques stem that 7000x + 10000y = 2300000 --> Eq. 1

From statement 2 we know that 10000y = 200000 + 7000x ---> Eq. 2

Let's put them together
7000x + 200000 + 7000x = 2300000
                                  x  = 150
We can put the value of x in Eq. 1 and get
7000*150 + 10000y = 2300000
                          y = 125

Hence, Statement 2 is sufficient  
Answer is D

Shubhradeep · Answer

Option D

Statement 1: 
x+y = 275  
=> 10x + 10y = 2750 ...(I) 
=> 7x + 10y = 2300 ...(II) 
 NOTE: we have reduced 3 zeros from each side

(I)-(II) => 3x = 450 => x = 150 and y=125

Sufficient

Statement 2: 
Suppose money awarded in $7000 is y
So, money awarded in $10000 is y+200000

So, y+y+200 = 2300  
=> y= 1050
So, money awarded in $7000 =  \frac{1050}{7}  = 150
And, money awarded in $10000 =  \frac{(1050+200)}{7}  = 125

Sufficient

Either statement is sufficient

Hence, option D

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

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