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# Jack bought one shampoo, two toothpastes, and two

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Current Student
Joined: 11 May 2008
Posts: 552
Jack bought one shampoo, two toothpastes, and two [#permalink]

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29 Jul 2008, 10:20
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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.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Director
Joined: 27 May 2008
Posts: 539

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29 Jul 2008, 10:32
arjtryarjtry wrote:
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.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

plugging numbers is my approach

st 1 : brush : paste : shapoo
2*1 + 2*2 + 7
2*2 + 2*1 + 7
so no item is \$4 and we have two possible prives for brush... not suff

St2 :
b<p<s

if b = 1
2*1 + 2*2 + 7 = 13 --1<2<7
2*1 + 2*3 + 5 = 13 --1<3<5

if b = 2
2*2 + 2*3 + 3 = 13 --2<3=3 .... does not satisfy ..
for any value of b>1 there is no possible combination ... Suff .. option B
Senior Manager
Joined: 23 May 2006
Posts: 311

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29 Jul 2008, 10:35
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?

From the Q you will get the equation: S +2T + 2B = 13

S1. No item priced of \$4.

See how may ways you can get 13 without pricing any item at \$4
First way: 3+ 2(3)+ 2(2) = 3+6+4 = 13
Second way: 5 + 2(2) + 2(2) = 5+4+4 = 13
Third way: 5+ 2(1) + 2(3) = 5+2+6 = 13
7 +2(2) + 2(1) = 13
Hence Maybe case so AD are out

S2 A shampoo is more expensive than toothpaste, and toothpaste is more expensive than a toothbrush.
First way: 5 + 2(3) + 2(1) = 5+6+2 = 13 ; only one way to satisfy the eq
Second way 7 +2(2) + 2(1) = 13
IMO B

Last edited by x97agarwal on 29 Jul 2008, 11:22, edited 3 times in total.
Senior Manager
Joined: 23 May 2006
Posts: 311

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29 Jul 2008, 10:43
arjtryarjtry wrote:
OA b

I got B the first time, however after a second look it looks like E.

What is the source of your Question and is there an official explanation since I cannot see the error in durgesh's or my answer.
Current Student
Joined: 11 May 2008
Posts: 552

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29 Jul 2008, 10:48
x97agarwal wrote:
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?

From the Q you will get the equation: S +2T + 2B = 13

S1. No item priced of \$4.

See how may ways you can get 13 without pricing any item at \$4
First way: 3+ 2(3)+ 2(2) = 3+6+4 = 13
Second way: 5 + 2(2) + 2(2) = 5+4+4 = 13
Third way: 5+ 2(1) + 2(3) = 5+2+6 = 13
7 +2(2) + 2(1) = 13
Hence Maybe case so AD are out

S2 A shampoo is more expensive than toothpaste, and toothpaste is more expensive than a toothbrush.
First way: 5 + 2(3) + 2(1) = 5+6+2 = 13 ; only one way to satisfy the eq
Second way 7 +2(2) + 2(1) = 13
Maybe so B is out

Combining you still get two values so IMO E

you ur self have got the ans as 1 for the brush in both 1) and 2) of stat 2
Senior Manager
Joined: 23 May 2006
Posts: 311

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29 Jul 2008, 11:21
arjtryarjtry wrote:
x97agarwal wrote:
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?

From the Q you will get the equation: S +2T + 2B = 13

S1. No item priced of \$4.

See how may ways you can get 13 without pricing any item at \$4
First way: 3+ 2(3)+ 2(2) = 3+6+4 = 13
Second way: 5 + 2(2) + 2(2) = 5+4+4 = 13
Third way: 5+ 2(1) + 2(3) = 5+2+6 = 13
7 +2(2) + 2(1) = 13
Hence Maybe case so AD are out

S2 A shampoo is more expensive than toothpaste, and toothpaste is more expensive than a toothbrush.
First way: 5 + 2(3) + 2(1) = 5+6+2 = 13 ; only one way to satisfy the eq
Second way 7 +2(2) + 2(1) = 13
Maybe so B is out

Combining you still get two values so IMO E

you ur self have got the ans as 1 for the brush in both 1) and 2) of stat 2

Thanks, overlooked it. I am trying to do multiple things at once.

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: PRICE DS   [#permalink] 29 Jul 2008, 11:21
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