Jack bought one shampoo, two toothpastes, and two toothbrushes. If the

Let the price of shampoo, toothpastes, and toothbrushes be s, t and b respectively.

Given : s+2t+2b=13
As a side note, what does the equation tell you ? : It tells us that s is odd and t & b cannot be more than 5.

(1) No item priced of $4.
Various combinations possible.
s+2t+2b=13 => \(5+2*2+2*2=13\) OR \(1+2*5+2*1=13\)

(2) A shampoo is more expensive than toothpaste, and toothpaste is more expensive than a toothbrush.
s>t>b..... s is ODD
So minimum value of s=3, t=2 and b=1.....s+2t+2b=13 => \(3+2*2+2*1=9\neq 13\)
\(s\neq{3}\)
Next possible value of s=5.....s+2t+2b=13 => \(5+2(t+b)=13......t+b=4\). As t>b, only possible values are 3 and 1.
Next possible value of s=7.....s+2t+2b=13 => \(7+2(t+b)=13......t+b=3\). As t>b, only possible values are 2 and 1.
Next possible value of s=9.....s+2t+2b=13 => \(9+2(t+b)=13......t+b=2\). As t>b, No distinct values of t and b possible.
So possibilities for {s,t,b}={5,3,1} and {s,t,b}={7,2,1}
In each case, the value of b is 1.
Sufficient

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?

Given, x+ 2y+ 2z= 13 , please note: x= odd no. always

Stat1: No item priced of $4.
x+ 2y+ 2z= 13
1---3----3
3---3----2
-----------
So, z= toothbrushes can have many values..Not sufficient.

Stat2: A shampoo is more expensive than toothpaste, and 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 (possible, as x>y>z); z= toothbrush = 1
7---2---1 (possible, as x>y>z); z= toothbrush = 1
9---1---1 (not possible, as x>y>z)

So, Sufficient.. I think B.