Jack Bought One Shampoo, Two Toothpastes, and Two Toothbrushes GMAT Data Sufficiency

Question: Jack bought one shampoo, two toothpastes, and two toothbrushes. If the total cost is $13, and all items have an integer price, in dollars, what is the price for the toothbrush?

1. No item priced of $4
2. A shampoo is more expensive than toothpaste, and toothpaste is more expensive than a toothbrush

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Approach Solution (1):
s + 2tp + 2tb = 13
S1:
Case 1: s = 3; tp = 2; tb = 3
Case 2: s = 3; tp = 3; tb = 2
Insufficient
S2:
s > tp > tb
Minimum possible price of one shampoo, two toothpastes, and two toothbrushes if tb = 2, is = 4 + 2*3 + 2*2 = 14 > 13
Hence price of toothbrush has to be 1
Sufficient
Correct option: B

Approach Solution (2):
Given: x + 2y + 2z = 13
x = odd number always
S1: No item priced of $4
x + 2y + 2z = 13
1 --- 3 --- 3
3 --- 3 --- 2
So, z = toothbrushes can have many values
Not sufficient
S2: A shampoo is more expensive than toothpaste, and the toothpaste is more expensive than a toothbrush
x > y > z
x + 2y + 2z = 13
1 --- 3 --- 3 (not possible, as x > y > z)
3 --- 3 --- 2 (not possible, as x > y > z)
5 --- 3 --- 1 (not possible, as x > y > z); z = toothbrush = 1
7 --- 2 --- 1 (not possible, as x > y > z); z = toothbrush = 1
9 --- 1 --- 1 (not possible, as x > y > z)
Sufficient
Correct option: B

Approach Solution (3):
(1) No item priced of $4
The other items detail is not known
Not sufficient
(2) A shampoo is more expensive than toothpaste, and toothpaste is more expensive than a toothbrush
Possible combinations:
A. Shampoo = $7
Toothpaste = $2 each
Toothbrush = $1 each
B. Shampoo = $5
Toothpaste = $3 each
Toothbrush = $1 each
Toothbrush is always $1 each
Sufficient
Correct option: B

“Jack bought one shampoo, two toothpastes, and two toothbrushes. If the total cost is $13, and all items have an integer price, in dollars, what is the price for the toothbrush?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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