Mr. Wilson bought some white chocolates, which cost $2.50 each, and so

Question

Mr. Wilson bought some white chocolates, which cost $2.50 each, and some brown chocolates, which cost $3.50 each, for Thanksgiving. The total amount paid by Mr. Wilson to the shopkeeper was $40. What is the ratio of the number of white chocolates to that of brown chocolates?

A. 5 : 3
B. 11 : 9
C. 2 : 5
D. 9 : 5
E. Cannot be determined

(Source=TCYOnline)

A. 5 : 3
B. 11 : 9
C. 2 : 5
D. 9 : 5
E. Cannot be determined

(Source=TCYOnline)

Amity007 · Answer

Right Answer Explanation / Suggested Answer :
Let the number of white chocolates be x and the number of brown chocolates be y.
According to the question,
2.50x + 3.50y = 40
Or 0.5x + 0.7y = 8
Out of the given options, only '9 : 5' satisfies the equation.
Hence, required ratio = 9 : 5

arushi118 · Answer

x = 2 and y = 10 also satisfies the equation. So how to determine that it is 9:5 and not 1:5?

Edskore · Answer

Great catch, arushi118 — this is actually one of the most common traps on GMAT PS, and you're thinking about it exactly right.

You're correct that x = 2, y = 10 also satisfies 2.5x + 3.5y = 40. So does x = 9, y = 5. With one equation and two unknowns, there are infinitely many solutions in theory. On its own, this equation is underdetermined — a concept the GMAT tests frequently.

Here's why the answer is still D (9:5): look at what the question is actually asking. It gives you five specific ratio options. The GMAT is telling you that only one of those ratios produces a valid whole-number solution (since you can't buy 2.3 chocolates).

Let's check both integer solutions:

- x = 9, y = 5 → ratio = 9:5 → appears as option D ✓
- x = 2, y = 10 → ratio = 1:5 → NOT in the answer choices

So x = 2, y = 10 is a valid algebraic solution but doesn't match any answer choice, which eliminates it in a PS context. The answer choices themselves act as an additional constraint, narrowing the solution space when algebra alone won't give a unique answer.

The common trap: students try to solve this purely algebraically, see multiple solutions, and panic. But in PS, if the question has multiple valid setups yet only one answer choice survives, that's your answer.

Takeaway: On PS questions with underdetermined systems, never forget that the five answer choices are part of the problem — treat them as a constraint, not just a final check.

jotirmoy81 · Answer

Let, Number of white chocolates = w
 Number of brown chocolates = b
Given prices:
 White chocolate = $2.50 each
 Brown chocolate = $3.50 each
 Total cost = $40
So we form the equation:
 2.5w+3.5b=40
 25w+35b=400 (multiply both side by 10)
 5w+7b=80 (divided both side by 5)

so, we can write w= /

Now, if we put the value of brown ratio from the answer choice; 
we only find the integer value of w=9 when b=5.

The other value of b= 3/9 gives us a fraction value of w, and  chocolate can not buy as a fraction .
So, 9:5 will be the answer. (option D)

TomoProduct · Answer

I get it, but I think this is a bit too much. Dont think GMAT will trap us this much. Cause this is very deceiving.

vasu1104 · Answer

say total white chocolate = w, price for white= 2.5$ each
brown chocolates =b, price for brown = 3.5$ each

2.5w + 3.5b= 40
25w + 35b = 400
5w + 7b = 80
w= (80/5) -7b/5
w= 16 -(7/5)b

now b must be divisible by 5. so try some value of b and get value of w.
when b= 5 we get w = 9
when b= 10 we get w= 2
when b=15 we get w= -5. this is not possible.

we need to find the ration w:b
we have two option. 9:5 and 2:10
from given choice, ans is D

Mr. Wilson bought some white chocolates, which cost $2.50 each, and so

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Mr. Wilson bought some white chocolates, which cost $2.50 each, and so

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