A casino pays players using purple and orange chips; each

Question

A casino pays players using purple and orange chips; each purple chip is worth p dollars, and each orange chip is worth n dollars. If p and n are integers, what is the combined value of two purple chip and one orange chip?

(1) The combined value of five purple chips and seven orange chips is 53 dollars.
(2) The combined value of six purple chips and three orange chips is 42 dollars.

Source: Manhattan GMAT - Thursdays with Ron (September 13, 2012)

Marcab · Accepted Answer

The question is:what is the value of 2p+n?

Statement 1: 5p+7n=53
since it is given that p and n are integers, therefore  p=(53-7n)/5 . For p to be an integer, 53-7n has to be an integer or 7n has to be such a number which ends up with 8 at its units place. Only  7x4=28  does that. Hence n=4, and p comes out as 5.
Sufficient.

Statement 2: divide the expression by 3. 
Sufficient.

+1D

Bunuel · Answer

A casino pays players using purple and orange chips; each purple chip is worth p dollars, and each orange chip is worth n dollars. If p and n are integers, what is the combined value of two purple chip and one orange chip?

Questions: 2p+n=?

(1) The combined value of five purple chips and seven orange chips is 53 dollars --> $5p+7n=53$ --> $5p=53-7n$. Thus we have that 53 minus multiple of 7 must be a multiple of 5. Only positive integer values of p and n which satisfy this are 5 and 4, respectively. Sufficient.

(2) The combined value of six purple chips and three orange chips is 42 dollars --> $6p+3n=42$ --> reduce by 3: $2p+n=14$. Sufficient.

Answer: D.

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Hope it helps.

nicktim · Answer

Thanks a lot for your help, Marcab & Bunuel. My apologies regarding the classification issue.

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

Remember the relation between the Variable Approach, and Common Mistake Types 3 and 4 (A and B)[Watch lessons on our website to master these approaches and tips]

Step 1: Apply Variable Approach(VA)

Step II: After applying VA, if C is the answer, check whether the question is key questions.

StepIII: If the question is not a key question, choose C as the probable answer, but if the question is a key question, apply CMT 3 and 4 (A or B).

Step IV: If CMT3 or 4 (A or B) is applied, choose either A, B, or D.

Let's apply CMT (2), which says there should be only one answer for the condition to be sufficient. Also, this is an integer question and, therefore, we will have to apply CMT 3 and 4 (A or B).

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find the value of 2purple chips + 1 orange chip.

=> Purple($p) and Orange($n) - where 'p' and 'n' are integers

Second and the third step of Variable Approach: From the original condition, we have 2 variables (p and n). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

But we know that this is a key question [Integer question] and if we get an easy C as an answer, we will choose A or B.

Let’s take a look at each condition.

Condition(1) tells us that 5p + 7n = 53.

=> 5p = 53 - 7n. The result should be divisible by 5

=> For n = 4 , 5p = 53 - 7(4) = 53 - 28 = 25. => p = 5.

Since the answer is unique, the condition is sufficient by CMT 2.

Condition(2) tells us that 6p + 3n = 42.

=> Dividing boththe sides by '3' => 2p + n = 14

Since the answer is unique, the condition is sufficient by CMT 2.

Condition (1) and Condition (2) alone are sufficient.

So, D is the correct answer.

Answer: D

daniformic · Answer

S1: 5p+7o=53
I need 3 as unit digit -> 5+8=13
So, 5*5+7*4=53 YES

S2: 6p+3o=42
I have to find the value of 2p+o:
2p+o=14

Answer -> D

Goldenfuture · Answer

Statement 2 is easy to kill divide by 3 and what we are asking is the answer
for statement 1 note 5P +7o = 53
If p and o are integers then 53- 5o is divisible by 7
53 - 5 = 48
53-10 = 43
53-15 = 38
53-20 = 33
53-25 = 28 - yesssss
53-30 = 23
53-35 = 18
53-40= 13 no
53-45 = 8 no
53-50 = no
Only 1 case bingo

A casino pays players using purple and orange chips; each

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