Three friends are buying a gift for a friend. Declan contributes 4 dol

Question

Three friends are buying a gift for a friend. Declan contributes 4 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift?

A. 48
B. 54
C. 60
D. 66
E. 72

Kudos for a correct solution.

A. 48 
B. 54
C. 60
D. 66
E. 72

sterling19 · Answer

Declan = D, Ed = E, Frank = F
t = total

D + E + F = t
(t/4 + 4) + (t/3 - 1) + 22 = t
t = 25 + (7t/12)
12t = 25(12) + 7t
5t = 5*5(12)
t = 60

The correct answer is C.

KS15 · Answer

x/4+4+x/3-1+22=x
Answer=C

PareshGmat · Answer

Answer = C = 60

Let total contribution = x

Declan ........................... Ed ...................... Frank ...................... Total

\frac{x}{4} + 4 .........................  \frac{x}{3} - 1  ................... 22 .......................... x

Total =  x = \frac{x}{4} + 4 + \frac{x}{3} - 1 + 22

x = 60

smashbiker84 · Answer

plugging in the answers and backsolving or solving by algebra..either way 60 is the only solution..ans (c)
preferred to plug in as 54 and 66 went straight out since they are not divisible by 4. the gift cost would not be a whole number in that case.Experts- please advise if i am not adopting the right strategy for such questions.

EMPOWERgmatRichC · Answer

Hi smashbiker84,

You've shown some real "flexible" thinking by using the answers to your advantage (and knowing your Number Properties). Assuming that you confirmed that the correct answer was correct, then your method is just as viable as any other. I typically TEST THE ANSWERS 2-3 times per Test, so it's a skill that can be quite helpful.

As a slight warning though, the prompt never stated that each of the 3 friends contributed an integer number of dollars. As an example, 54 can be divided into fourths (54/4 = 13.50), so Declan COULD have contributed 4 dollars more than $13.50 (4 + 13.50 = $17.50). On rarer versions of this question that are far more complex, decimals could be involved (again, albeit rarely).

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION friendsbuyagift_text(1).png

lalania1 · Answer

In this question I find that algebra is easier for me. If someone can explain to me how to best distinguish between backsolving and algebra before solving a question, that would be great!
My first attempt was backsolving but i got it wrong took me too long.

abhimahna · Answer

Let the total price of gift = 12x

D pays 3x + 4
E pays 4x - 1

Therefore , F pays 12x - (3x + 4 + 4x -1 ) = 12

or x = 5.

Hence, total cost = 12 * 5 = 60. Answer C.

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Three friends are buying a gift for a friend. Declan contributes 4 dol

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