If Pei ordered a total of 63 bottles of cola, root beer, and ginger

Question

If Pei ordered a total of 63 bottles of cola, root beer, and ginger ale for a party, how many bottles of cola did she order?

(1) The number of bottles of root beer that Pei ordered was 80 percent of the number of bottles of ginger ale that she ordered.

(2) The number of bottles of cola that Pei ordered was 75 percent of the total number of bottles of root beer and ginger ale that she ordered.

ID 00763

Bunuel · Answer

If Pei ordered a total of 63 bottles of Cola, Root Beer and Ginger Ale for a part. How many Cola bottles did she order?

Given: {Cola} + {Beer} + {Ale} = 63.
Question: {Cola} = ?

(1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered --> {Beer} = 0.8{Ale} --> 5*{Beer} = 4*{Ale} ({Beer} is a multiple of 4 and {Ale} is a multiple of 5). If {Beer} = 4 and {Ale} = 5, then {Cola} = 54 but if {Beer} = 8 and {Ale} = 10, then {Cola} = 45. Not sufficient.

(2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered --> {Cola} = 0.75*({Beer} + {Ale}) --> {Beer} + {Ale} = 4/3*{Cola} --> {Cola} + 4/3*{Cola} = 63. We can solve for C. Sufficient.

Answer: B.

sagnik242 · Answer

Question : How did you get from 0.8 Ale to 5 Beer , and then to the 4 ale, beer ? Also, how did you get from 0,75 beer ale to 4/3 cola?

whitehalo · Answer

Hi sagnik242,

let me try to help.
Beer = 0.8 Ale
Beer =  \frac{8}{10}  Ale
10 Beer = 8 Ale (multiply the entire expression with 10)
5 Beer = 4 Ale (simplify by dividing the entire expression with 2)

same goes with 0,75 beer ale to 4/3 cola. hope that was helpful :D

Raihanuddin · Answer

This question could be very tricky if total number of bottles bought was between 10 and 17. A could be sufficient.

When I solved A, I didn't use any equation. I tried to think logically that Number of cola bottle could be any number if I different number of Ginger ale bottles.

But after looking the official solution, I realized that my thought process for A could be dangerous. I have to actually form equation in this type of situation.

BLTN · Answer

Take into consideration the av.time taken by participants, I have doubt that the first statement was fully tested. Or I do it too slowly

C + RB + GA = 63 Statement 1 RB = 8/10 of GA = 4/5 of GA C + 4/5GA + GA = 63 5C + 9GA = 315 C = 9(35-GA)/5 Hence, C is a multiple of 9, yet it can by any number within aforementioned restrictions. The quibble here is if those numbers were primes, the probability that we can get correct answer is very high. Statement 2 is indeed sufficient, we get sum of RB + GA, and, thus, we can deduct it from total and get the result.

egmat · Answer

Here we're working with a system of equations problem disguised as a data sufficiency question – these can be tricky because you need to recognize exactly how many constraints you need to solve for unique values.

Let's think through this systematically. You have three unknowns (cola, root beer, ginger ale) and one given constraint:
 C + R + G = 63

Since you need as many equations as unknowns to solve uniquely, you'll need 2 more independent constraints.

For Statement (1): 
"Root beer = 80% of ginger ale" gives us:  R = 0.8G

Now you can substitute into the main equation:
 C + 0.8G + G = 63 
 C + 1.8G = 63

Notice how you still have two unknowns (C and G) but only one equation? This means multiple solutions are possible. For instance, if G = 10, then C = 45. If G = 20, then C = 27. Statement (1) alone isn't sufficient.

For Statement (2): 
"Cola = 75% of (root beer + ginger ale)" gives us:  C = 0.75(R + G)

Here's the key insight: Since  C + R + G = 63 , you know that  R + G = 63 - C

Substituting this into your Statement (2) equation:
 C = 0.75(63 - C) 
 C = 47.25 - 0.75C 
 1.75C = 47.25 
 C = 27

You get exactly one solution! Statement (2) alone is sufficient.

Answer: B

You can check out the  step-by-step solution on Neuron by e-GMAT  to master the systematic framework for identifying when you have sufficient constraints in data sufficiency problems. You can also explore other GMAT official questions with detailed solutions and practice the pattern recognition techniques  here .

If Pei ordered a total of 63 bottles of cola, root beer, and ginger

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GMAT Data Sufficiency (DS) Questions

If Pei ordered a total of 63 bottles of cola, root beer, and ginger

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