At a bookstore promotion, each of five customers won a chance

Question

At a bookstore promotion, each of five customers won a chance to receive a discount. For each customer, five sealed envelopes were prepared. The five envelopes prepared for any customer contained the discounts $10, $20, $30, $40, and $60, one discount per envelope. If each customer selected one of the five envelopes prepared for that customer, did any customer receive the $60 discount?

(1) The sum of the discounts received by the five customers was $150.
(2) No two customers received the same discount.

M47-189

Bunuel · Accepted Answer

GMAT Club Official Solution:

At a bookstore promotion, each of five customers won a chance to receive a discount. For each customer, five sealed envelopes were prepared. The five envelopes prepared for any customer contained the discounts $10, $20, $30, $40, and $60, one discount per envelope. If each customer selected one of the five envelopes prepared for that customer, did any customer receive the $60 discount?

(1) The sum of the discounts received by the five customers was $150.

Let’s check whether the sum of the discounts can be $150 both with and without any customer receiving the $60 discount.

• Without the $60 discount:

30 + 30 + 30 + 30 + 30 = 150

So it is possible that no customer received the $60 discount.

• With the $60 discount:

60 + 40 + 20 + 20 + 10 = 150

So it is also possible that at least one customer received the $60 discount.

Not sufficient.

(2) No two customers received the same discount.

There are five customers and five possible discount amounts:

$10, $20, $30, $40, and $60

If no two customers received the same discount, then the five customers must have received all five discount amounts. Therefore, one customer received the $60 discount.

Sufficient.

Answer: B.

scared · Answer

Consider statement 1:
sum = 150;
is it possible to reach 150 without 60?
40+40+30+20+20= 150;
Yes;
is it possible with 60?
60+40+20+20+10=150;
thus the statement is insufficient.
Consider statement 2: 
No two customers received the same discount; 
therefore one person will get one of the 5 outcomes.
this is sufficient alone. 
the answer : B

vasu1104 · Answer

there are five people. each has 5 choice of envelope but can select only one envelope. 
the price in each envelope is 10,20,30,40,60

now we need to find did any one get 60$ discount?

S-1
there are few ways we can get the sum of 150.
20+20+40+10+60 =150
30+30+30+30+30= 150
20 +40 +40 +40 +10=150

so we can't say fro guarantee that yes some one got 60$.
not sufficient.

S-2
that means everyone has different envelope and since we only have five envelope that means someone did get 60$ envelope.
this is sufficient.

Choice B

At a bookstore promotion, each of five customers won a chance

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GMAT Data Sufficiency (DS) Questions

At a bookstore promotion, each of five customers won a chance

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