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?
- 48
- 54
- 60
- 66
- 72
Correct Answer: C
Solution and Explanation
Approach Solution 1:
It is asked What is the cost of the gift If Three friends are buying a gift for a friend.Lets solve this question using the reasoning approach-
Let Declan be D, Ed be E, Frank be F and,
Total be T
Evaluating it further-
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 cost of the gift is 60 dollar
Approach Solution 2:
There is another approach to solve this question-
Let us solve this question-
Let's say the gift costs x dollars.
Since Declan contributes 4 dollars more than the \(\frac{1}{4}\)gift's cost,
As a result, Declan's contribution = \(\frac{x}{4}\)+4
In addition, Ed contributes one dollar less than the \(\frac{1}{3}\)cost of the gift.
As a result, Ed's contribution = \(\frac{x}{3}\)-1
Frank contributes the remaining 22 dollars once more.
Since, Only three people contributed.
Therefore total price of cost = \(\frac{x}{4}\)+ 4 + \(\frac{x}{3}\)-1+ 22
Let us evaluate further-
= \(\frac{3x+4x}{12}\)+25
= \(\frac{7x}{12}\)+25
= \(\frac{7x}{12}\)+25=x
= \(\frac{7x}{12}\)=x-25
7x = 12x-300
7x = 12x-300
300= 12x-7x
300 = 5x
x = \(\frac{300}{5}\)
x = 60
The cost of the gift is 60 dollar
Approach Solution 3:
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.
“Three friends are buying a gift for a friend. Declan contributes 4 dollars”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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