Each of six students, four girls and two boys, spent an average of

Question

Each of six students, four girls and two boys, spent an average of $60 on books. If the girls spent a total amount of $300, how much did boy X and Y spends on books?

(1) X spent twice as much as Y spent on books.
(2) X spent $20 more than Y on books.

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Sonatomar · Answer

X=2Y

And we already know:

X+Y=60

Substitute:

2Y+Y=60 
3Y=60 , Y=20 and X=40

✅ We can determine both.X spent $20 more than Y.

So:

X=Y+20

And:

$X+Y=60 $

Therefore:

(Y+20)+Y=60

2Y=40 Y=20 
 X=40

✅ We can determine both.D — Each statement alone is sufficient

SageGMATtutor · Answer

With DS problems, take a moment to review the situation to see if there's any simplification or useful reframing to do  before  assessing the statements. Here, the word 'average' is a clue that we can find the total amount of money spent on books. Since there are 6 students and the average spend was $60, the total spent was $360. Further, since the girls spend $300, this means that the two boys spent $60 between them. This is a much more useful starting point for assessing the statements.

We could translate the statements into algebra, but I would consider that unneccessary here. I would encourage students to become familiar enough with certain generic situations to be able to assess the statements without algebra. For statement 1, we have a ratio of spending. This, along with the total spent, is sufficient information to calculate what X and Y spent indivitually. The numbers here are easy enough to actually work out the numberical answer (strictly speaking, not necessary, but often quite a useful check): X spent $40 and Y spent $20. Statement 1 alone is sufficient, so eliminate answers BCE from your answer grid.

For statement 2, we have another generic situation: we know the total and the difference of 2 numbers, which is sufficient information to calculate what X and Y spent individually. Again, you can check your logic by calculating the numbers, which should be consistent with statement 1. Statement 2 alone is also sufficient, so the answer to the problem is D.

KarishmaB · Answer

Infer as you go along - each of 6 students spent an average of $60. So the 6 together spent $360. 
The 4 girls spent $300 so the 2 boys together spent $60.

(1) X spent twice as much as Y spent on books.

Since X + Y total is 60, if X spent twice that of Y, X must have spent 40 and Y must have spent 20. 
Sufficient alone.

(2) X spent $20 more than Y on books.

Again, this means X spent 40 and Y spent 20. 
Sufficient alone.

Answer (D)

You can work on it algebraically if you wish. The question stem tells us X + Y = 60
Stmnt 1 tells us that X = 2Y and statement 2 tells us that X - Y = 20. So we have 2 unknowns and 2 distinct equations with each stmnt alone.

Bananaa · Answer

Average $60 per person → 6ppl = $360
→ x+y=60
(1) x=2y → sufficient to calculate X and Y
(2) X =y+20 → sufficient to calculate X and Y
Answer D

Each of six students, four girls and two boys, spent an average of

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GMAT Data Sufficiency (DS) Questions

­Each of six students, four girls and two boys, spent an average of

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Each of six students, four girls and two boys, spent an average of