A neighborhood library purchased 45 paperback copies of a novel at an

Question

A neighborhood library purchased 45 paperback copies of a novel at an average price of $16 per copy. It then decided to buy 15 hardcover copies of the same novel as well. Was the average (arithmetic mean) price per copy of all 60 books less than $22?

(1) The total cost of the 15 hardcover copies bought was more than $550 
(2) Each hardcover copy cost less than $40.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A neighborhood library purchased 45 paperback copies of a novel at an average price of $16 per copy. It then decided to buy 15 hardcover copies of the same novel as well. Was the average (arithmetic mean) price per copy of all 60 books less than $22?

Let the total cost of the 15 hardcover copies be H.

The 45 paperback copies cost 45 * 16 = 720

For the average price of all 60 books to be less than $22, the total cost of all 60 books must be less than 60 * 22 = 1320

So we need: 
720 + H < 1320
H < 600

So the question is really asking:

Is the total cost of the 15 hardcover copies less than $600?

(1) The total cost of the 15 hardcover copies bought was more than $550

This says H > 550. That is not enough to conclude whether H < 600.

Not sufficient.

(2) Each hardcover copy cost less than $40.

Each of the 15 hardcover copies cost less than $40. So:

H < 15 * 40 = 600

That is exactly what we need.

Sufficient.

Answer: B.

rajdeep212003 · Answer

Given:

45 books at $16 each 
→ total = 45 × 16 = 720

15 hardcover books → let total cost = H

Total books = 60

---

Question:

Average < 22

⇒ (720 + H) / 60 < 22 
⇒ 720 + H < 1320 
⇒ H < 600

---

So we need:

H < 600

---

Check statements:

(1) H > 550

→ could be 560 → satisfies 
→ could be 590 → satisfies 
→ could be 610 → not allowed

So we can’t fix a definite answer

❌ Not sufficient

---

(2) Each < 40

So total H < 15 × 40 = 600

⇒ H < 600

This directly satisfies the condition

✔️ Sufficient

---

Final Answer:

B

---

Hope this helps. 
If anything feels off, feel free to tag me — we can go through it.

– Rajdeep

Adit_ · Answer

Statement 1:
Taking the critical point that is 550 and use average formula:
We see that the the average is less than 22. But when greater than 550, avg could be more than 22.
INSUFFICIENT.

Statement 2:
Taking 40*15 = 600.
Using avg formula we see that we get:
Avg = 22.
But each is less than 40.
Thus avg is less than 22.
SUFFICIENT.

Answer:  Option B

BongBideshini · Answer

Let the cost of each hardcover copy be p. Then: (720 + 15p) / 60 < 22 720 + 15p < 1320 15p < 600 p < 40 So the question becomes: Is p < 40? Statement (1) The total cost of 15 hardcovers was more than $550 15p > 550 p > 36.67 Could be: p = 38=> Yes p = 45=> No Not sufficient Statement (2) Each hardcover copy costs less than $40 p < 40 This directly answers the question. Sufficient Ans B

A neighborhood library purchased 45 paperback copies of a novel at an

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