A hardware store purchased x identical standard flashlights at $5 each

Question

A hardware store purchased x identical standard flashlights at $5 each and y identical deluxe flashlights at $7 each. The total cost to the store for both types of flashlights was $92. What is the ratio of x to y ?

A. 5 to 7
B. 7 to 5
C. 5 to 1
D. 17 to 1
E. It cannot be determined from the information given.

A. 5 to 7
B. 7 to 5
C. 5 to 1
D. 17 to 1
E. It cannot be determined from the information given.

KSBGC · Answer

Back solve the question .

Option D matches.

17*5 + 1*7 = 92

The best answer is D.

Ypsychotic · Answer

In mathematical terms, the question becomes 5*x+7*y=92, there is no other information, so let's find out how unit digit can be achieved. 5 will produce only 0 or 5 as the unit digit. Say, unit digit of 5x is 0, that means unit digit of 7y should be 2, that is possible for y=6, putting it in the equation y=6 and x=5 (92-7*6/10) Ratio is 5:6, 
The other case where unit digit of 5x is 5, unit digit of 7y should be 7, putting in the equation, y=1 and x=17, Ratio is 17:1, also one of the options.

Since there is ambiguity, answer IMO is E.

abhimanyujain1711 · Answer

hi Bunuel,
what are your comments on the above?

tapasgupta · Answer

The equation becomes 5x+7y=92

We need to calculate x/y.

out of the options, Option D will give the value 92.

There can be other value of x/y. If the option D was not given then the correct answer could be E.

But in this case, we are getting the value.

Bunuel, Please advise.

ksrutisagar · Answer

The equation we get is 5x + 7y = 92

From the answer choices x = 17 , y = 1 satisfies and ratio = 17/1
To get another value subtract 7 which is the coefficient of y in the equation from the previous value of x , so new value of x = 10
Add 5,the coefficient of x in the equation to the previous value of y, So new value of y = 6
It can be seen that 5(10) + 7(6) = 92
So, another value of the ratio = 10/6

So, Cannot be determined Choice E

tapasgupta · Answer

Hi ksrutisagar,

Thanks for helping.

But I have one question. Why do we require another value? The answer that you stated is not in the answer choice. Question asks about to find the ratio, we have the ratio. If this were DS question it would definitely answer E.

Please advise.

EgmatQuantExpert · Answer

Solution

• A hardware store purchased x identical standard flashlights at $5 each
 o And, y identical deluxe flashlights at $7 each. 
• The total cost to the store for both types of flashlights was $92.

To find:  
 • Ratio of x to y=?

Approach and Working:   
 • 5x+7y= 92
 o For x= 17, y=1
o For x= 10, y= 6
o For x= 3, y= 11

Hence, x:y cannot be determined form the given information.
Hence, the correct answer is option E.

Answer: E

ksrutisagar · Answer

IMO the question is slightly ambiguous. If it had been a "could be " question the answer would be 17/1 , but since the question is which of the following  is  the ratio, I think the answer is E

AdityaHongunti · Answer

I disagree with the question ... teh question is "what is the ratio x to y" ....it is not "WHAT MUST be the ratio"

It depends on an individual as to what he chooses as the value and for his value the ratio is true...so essentially his/her answer is right...
the question could be better worded as to either "what CAN be the ratio" or "what MUST be the ratio"

GMATGuruNY · Answer

Consider the following equation:
2x + 3y = 30.

If x and y are nonnegative integers, the following solutions are possible:
x=15, y=0
x=12, y=2
x=9, y=4
x=6, y=6
x=3, y=8
x=0, y=10

Notice the following:
The value of x changes in increments of 3 (the coefficient for y).
The value of y changes in increments of 2 (the coefficient for x).
This pattern will be exhibited by any fully reduced equation that has two variables constrained to nonnegative integers.

Bunuel

A hardware store purchased x identical standard flashlights at $5 each and y identical deluxe flashlights at $7 each. The total cost to the store for both types of flashlights was $92. What is the ratio of x to y ?

A. 5 to 7
B. 7 to 5
C. 5 to 1
D. 17 to 1
E. It cannot be determined from the information given.

5x + 7y = 92
Since 7*6 = 42, one possible solution will be yielded if 5x=50, as follows:
Case 1: x=10, y=6

As noted above:
x may change only in increments of 7 (the coefficient for y)
y may change only in increments of 5 (the coefficient for x)
Thus, two other cases are possible:
Case 2: x=10+7=17, y=6-5 = 1 --> x=17, y=1
Case 3: x=10-7=3, y=6+5 = 11 --> x=3, y=11

Since Cases 1, 2 and 3 will yield different values for x/y, the ratio of x to y cannot be determined.

Show Spoiler

E

For more practice with the approach used here, check my solutions for the following problems:
https://gmatclub.com/forum/eunice-sold- ... 02-20.html
https://gmatclub.com/forum/for-how-many ... 91382.html
https://gmatclub.com/forum/joanna-bough ... 43-20.html

MathRevolution · Answer

5x + 7y = 92

For various possible combinations of 'x' and 'y', the given equation will give a total of 92.

Example:

=> x = 17 and y = 1 = 5(17) + 7(1) = 92

=> x = 10 and y = 6 = 5(10) + 7(6) = 92

No unique value of 'x' and 'y' and hence no unique ratio value

Answer E

Basshead · Answer

5x + 7y = 92

If the multiple of 7 ends in  2 or 7 , then it's possible for x to take on multiple values.

7 - { 7 , 14, 21, 28, 35,  42 , 49, 56, 63, 70,  77 , 84, 91}

As we can see, y can be 1, 6, or 11, meaning 3 different values of x are possible.

Answer is E .

gmatcafe · Answer

+

5x+7y=92
x y
17 1
10 6

x/y=17:1 or x/y=10:6=5:3
So without additional information we cannot determine the ratio of x to y. E)

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A hardware store purchased x identical standard flashlights at $5 each

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