A school bookstore sold only two kinds of planners during orientation

Question

A school bookstore sold only two kinds of planners during orientation week: a basic planner for 8 euros and a deluxe planner for 11 euros. How many planners did the bookstore sell in total?

(1) The average (arithmetic mean) selling price per planner was 9 euros.

(2) The number of basic planners sold was twice the number of deluxe planners sold.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A school bookstore sold only two kinds of planners during orientation week: a basic planner for 8 euros and a deluxe planner for 11 euros. How many planners did the bookstore sell in total?

(1) The average (arithmetic mean) selling price per planner was 9 euros.

The average price was 9 euros, so

(8x + 11y)/(x + y) = 9

8x + 11y = 9x + 9y

2y = x

So (1) just tells us only that the number of basic planners sold was twice the number of deluxe planners sold. It does not tell us the total number sold. Not sufficient.

Another way to see the same thing is through distances from the average. The average is 9, which is 1 euro above 8 and 2 euros below 11. Therefore, the number of basic planners sold must be twice the number of 11-euro planners, so that the overall average is pulled closer to 8. But that still does not determine the total number sold. Not sufficient.

(2) The number of basic planners sold was twice the number of deluxe planners sold.

This statement directly tells us that the number of basic planners sold was twice the number of deluxe planners sold. But many totals are still possible. Not sufficient.

(1) + (2) Both statements give the same exact information. So combining them does not help. Not sufficient.

Answer: E.

Adit_ · Answer

Using the alligation method you can notice that both statement 1 and 2 give us the same result.
Statement 1 --> gives us the ratio 2:1
Statement 2 --> States it explicitly and adds nothing more.
Hence combining is also not enough.

Answer:  Option E

thisisakr · Answer

We have to find total number of planners sold?

1. Avg cost is 9

Basic is 8, delux is 11
 So Case 1: 2 basic 1 delux = 2*8+1*11=27 so avg is 27/3=9 
 Case 2: 4basic 2 delux = 4*8+2*11=54 so avg is 54/6=9

As you can we we get two answers for total number of planners sold both with avg 9 —-  insufficient

2. This statement says for no of basic planner sold is twice the delux one 
 If you take the example as in 1 we can see this doesn’t help or add any new information ——  insufficient

Both together are also not sufficient as they suggest the same this and end up giving same answer —  insufficient

So ans - E

KRKfan · Answer

Given: 
Price per basic planner: €8
Price per deluxe planner: €11

Question:  Number of total planners sold?

Statement 1:   The average (arithmetic mean) selling price per planner was 9 euros.

Let quantity of basic planners and deluxe planners sold be  B  and  D .

Avg price = Total Revenue / Total Quantity
 9 =   / (B + D)
 9(B + D) = 8B + 11D
 Solved further, we get
 B = 2D

We get a ratio of basic planners to deluxe planners to be  2:1 . But we don't get know if they sold 3 planners or 3,000 planners.

Statement 1 is  Not Sufficient .

Statement 2:  The number of basic planners sold was twice the number of deluxe planners sold.

Only the ratio of planners sold which has been calculated above is mentioned here, i.e.  2:1 . Still no data on the quantity of planners sold.

Statement 2 is  Not Sufficient .

Considering Statement 1 & 2 together,

Both statments tell exactly same thing, i.e.  2:1 . No new information is provided related to the quantity of planners sold after combining statements.

Combining Statements 1 & 2 is  Not Sufficient .

Correct answer is  E .

dostwal · Answer

(1) Let basic = b, deluxe = d.
Average price 9 ⇒ total revenue = 9(b + d).
But revenue also = 8b + 11d.
So 8b + 11d = 9b + 9d ⇒ b = 2d.
We only get a ratio, not exact values → insufficient.

(2) b = 2d gives only ratio again → insufficient.

Together: same equation b = 2d, still no absolute numbers → insufficient.

Answer: E

BongBideshini · Answer

1) bx(9-8)=dx(11-9)
-> b:d=2:1

2) b:d=2:1
Ans (E)

A school bookstore sold only two kinds of planners during orientation

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GMAT Data Sufficiency (DS) Questions

A school bookstore sold only two kinds of planners during orientation

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