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18 Aug 2026, 19:00
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D
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Difficulty:
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Question Stats:
67% (01:56) correct
33%
(02:09)
wrong
based on 156
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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.
(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.
19 Aug 2026, 00:03
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grants are x for 7k and y for 10k , total grants are 2300,000
7x+10y = 2300
1. totl 275 grnts
x+y=275
2 varbles 2 eqns , possible
2. 10k granyts r 200 more than 7k
10y- 7x=200
again 2 vrble 2 eqn posible
bth statements individually suff option D
7x+10y = 2300
1. totl 275 grnts
x+y=275
2 varbles 2 eqns , possible
2. 10k granyts r 200 more than 7k
10y- 7x=200
again 2 vrble 2 eqn posible
bth statements individually suff option D
21 Aug 2026, 19:44
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Bunuel
This question is a good example of the Equation Count Pattern: in a system of equations, as long as you have as many different linear equations as variables, you can solve for all variables.
To be linear, an equation can have no exponents greater than 1. To be different (or independent), it must be impossible for one equation to be put in the same form as another (for example, x + y = 1 and 2x + 2y = 2 are NOT different equations).
Let's represent the $7,000 grants as x and the $10,000 grants as y. Then we can say:
7,000x + 10,000y = 2,300,000 or simply 7x + 10y = 2300
So you have 1 equation, 2 variables.
The question asks: Is x > y?
Statement 1:
This tells us that:
x + y = 275
This is clearly a different linear equation from 7x + 10y = 2300; therefore you have 2 equations, 2 variables, and you can solve for both x and y. It doesn't matter whether x is greater than y: if it is, the answer is a definite YES, and if it isn't, the answer is a definite NO. Either way, you have one definite answer, so Statement 1 is sufficient.
Statement 2:
This can be translated as:
10y = 7x + 200
Though this looks closer to 7x + 10y = 2300, it is still a different equation and is therefore solvable using the same reasoning we used in Statement 1. If you're unsure, you can prove this by substituting directly for 10y:
7x + (7x + 200) = 2300
This can be solved for x, which will also allow you to solve for y. Sufficient.
The answer is D.
Look for the Equation Count Pattern in order to answer Data Sufficiency questions efficiently. Remember, you don't need to solve; you only need to know if you CAN solve for a statement to be sufficient.
