Three salespeople — A, B, and C — sold a total of 500 products among

Question

Three salespeople — A, B, and C — sold a total of 500 products among them during a particular month. During the month, did A sell more products than B sold as well as more products than C sold?

(1) A sold 166 products during the month.
(2) C sold 249 products during the month.

chetan2u · Accepted Answer

A+B+C=500.
We are looking for whether both A>B and A>C are true.

(1) A sold 166 products during the month.
So  A = 166 .....
 B+C=500-166=334 
 Let us make both B and C the least , and for that B=C.....
 2B=334...B=C=167 ....The moment we decrease one, say B, the other C will become greater than 167.
 Thus in all cases, AT LEAST one of B and C is greater than 166. 
Answer is NO.
Suff

(2) C sold 249 products during the month
A can be 500-249-1=250.... YES 
A can be 100..... NO 
Insuff

A

CrackverbalGMAT · Answer

We need to know if A > B and if A > C Statement 1: A sold 166 products during the month. From this we see that B + C sold 500 - 166 = 334 products. We can have B selling 200 and C selling 134, in which case A < B and A > C We can also have B selling 134 and C selling 200, in which case A > B and A < C Therefore Statement 1 Alone is Insufficient . Answer options could be B, C or E Statement 2: C sold 249 products during the month. From this we see that A + C sold 500 - 249 = 251 products. We can have A selling 200 and C selling 51, in which case A < B and A > C We can also have A selling 51 and B selling 200, in which case A < B and A < C We get conflicting answers. Therefore Statement 2 Alone is Insufficient . Combining Both Statements: A sells 166 products and C sells 249 products. Therefore B sells 500 - 249 - 166 = 85 products. Here A < B and A > C. This gives a definite answer. Therefore Both Statements together are sufficient . Option C Arun Kumar

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 3 variables and 1 Equation: Let the original condition in a DS question contain 3 variables and 1 Equation. Now, 3 variables and 1 Equation would generally require 2 more equations for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 2 more equations to match the numbers of variables and equations in the original condition, the logical answer is C.

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 whether A > B and A > C ?

Second and the third step of Variable Approach: From the original condition, we have 3 variables (A, B, and C) + 1 Equation (A +B + C = 500).To match the number of variables with the number of equations, we need 2 more equations. Since conditions (1) and (2) will provide 2 equations, C would most likely be the answer.

Let’s take look at both condition together.

Condition(1) tells us that A sold 166 products during the month.

Condition(2) tells us that C sold 249 products during the month.

=> A + B + C = 500

=> 166 + B + 249 = 500

=> B = 85 products

=> A (166) > B(85) and A (166) < C(249)

Since the answer is unique YES , both conditions combined together are sufficient by CMT 1.

Both conditions combined together are sufficient.

So, C is the correct answer.

Answer: C

SAVE TIME: By Variable Approach, when you know that we need two equations, we will directly combine the conditions to solve. We will save time in not checking the conditions individually.

Mona2019 · Answer

Bunuel  , could you please cross check the OA

Posted from my mobile device

Bunuel · Answer

The question asks whether A > B and A > C, so whether A sold more than each of B and C. From (1) it's not possible A to be more than B and C. The OA is A.

stne · Answer

(1) A sold 166 products during the month.

For A to be more than B and more than C, let B =165 and C=165 
So we get A+B+C= 496
So in spite of taking max. value of sales for B and C we cannot get total 500 sales if B and C have sales less than those of A.

Hence with 166 sales A cannot have more sales than B and more sales than C ( We need total 500 sales)

A is  SUFF.

(2) C sold 249 products during the month.

A \hspace{3mm} B \hspace{3mm}C 
250 1 \hspace{5mm} 249- A > B and A>C:True 
151 100 249- A > B and A>C: False 
 INSUFF.

Ans- A

Hope it's clear.

bumpbot · Answer

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Three salespeople — A, B, and C — sold a total of 500 products among

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