A shop only sells items for a whole number of dollars and

Question

A shop only sells items for a whole number of dollars and ninety-nine cents. Given that Mrs. Smith spent less than $50 at the shop, how many items did she buy? 
a. She paid $36.72 for the items that she bought. AD?
b. Had she bought another 72 items, she would have spent an exact number of dollars.

dr_sabr · Answer

a. She paid $36.72 for the items that she bought. AD? 

b. Had she bought another 72 items, she would have spent an exact number of dollars. 
 
a) Because the price is unknown, as it is x,99, and the question didn't indicate that the price is consistent for all items. A) insufficient.

b) Doesn't provide us with the total of what she paid. Insufficient

A and b, because of the we don't know about the consistency of the price, we can't know how many did she bought first

Therefore my answer is E.

Correct me if I am mistaken.

boksana · Answer

From A we can conclude that she bought 28 items
the reasoning is:

36.72=M+0.99*N=f(M, N) => N=28, so A is sufficient

sathya76 · Answer

Boksana,

Did you come up with 28 by brute force?

Can you explain further with your steps?

boksana · Answer

N could be only 28, because it's only 0.99*28=x.72 (x is not important) there are no more numbers for N

dr_sabr · Answer

But if the items have a different valus, like 2.99, 5.99. Isn't it impossible here to get a uniqe value. don't you think that the question here is not clear?? :roll:

boksana · Answer

Hope it's clear. Think about b. 


P.S. I'll explain my solution later

ashkg · Answer

Ans is D.

I must confess I saw the other posts and then came up with this solution. And I consulted a book to get the funda of getting value of ab.

let the number of items bought be ab ( value=10a+b)

x.99 * ab = 36.72

this means that x*ab = whole number
and 0.99 * ab = ends in 0.72

here's how we find the value of ab.

99
X ab
________

_______
72

9*b = ends in 2 => b=8

99
X a8
________
792
_______
72

now we have

9*a + 9 = ends in 7
=>
9(a+1) ends in 7

a+1 has to be 3
therefore a=2

so the number of items bought = ab = 28

So A is sufficient.

Now, let me try B.

Say ,she bought N number of items before. now she has (N+72) items.

(x.99)(N+72) = whole number = W

there are 2 digits in decimal place. for W to be a whole number
N+72 = 100 ( theres no other way)
so N=28.

So B is sufficient too.
Final answer is D.
I don't believe i did this ;-)

and don't ask me how much time i took !!!!!!!!

- ash

Don't you think we can get the answer by plugging in values ??
I would really prefer that !

and don't ask me how much time i took !!!!!!!! - ash Don't you think we can get the answer by plugging in values ?? I would really prefer that !

boksana · Answer

YES!! It's D. I mean my answer is D :-D

sid_477 · Answer

Guys i would beg to differ here! I think the answer shud be E
if 28 is the number of items in that case 36.72/28= 1.31 and not some x.99 value!

can somebody throw me a bone here!

sathya76 · Answer

Not all the 28 items are of equal value. Though the value of individual items is x.99 format.

dr_sabr · Answer

Isn't there any comments or explainations?

Paul · Answer

This question seemed rather obvious to me in the sense that you don't really need to know any formula to solve it. It should be D.
Say you buy 2 items at y.99$, the total will be x.98$
If you buy 3 items at y.99$, the total will be x.97$
x and y are unimportant since knowing that all items are priced at y.99$, and that he spent less than 50$, you only need to know the penny value to know how many items he bought.
A) if he's at x.72$, then we know he must have bought 28 items. Proof: do 28 * .99 and you get x.72$. He could not have bought 128 items  because max. spent is 50$ . If each item cost .99$, he would have been overbudget. Hence, you can safely say he bought 28 items.
B) with this, you know he bought 28 items for, (28+72) * .99 will give x.99$ and is sufficient.

A shop only sells items for a whole number of dollars and

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