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

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Intern
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A certain shop only sells items for a whole number of dollars and nine  [#permalink]

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New post 15 Jul 2018, 04:37
1
8
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A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

44% (02:13) correct 56% (02:24) wrong based on 176 sessions

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A certain shop only sells items for a whole number of dollars and ninety-nine cents. If Mrs. Jones spent less than $50 at the shop, how many items did she buy?

(1) She paid $36.72 for the items that she bought.

(2) Mrs. Jones did not spend more than $10.99 for any one item.


Can someone please explain the solution?
The question itself took me so long to understand.
Would one prefer to skip these kind of questions or spend more than 2 minutes trying to solve it?
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Re: how many items did she buy?  [#permalink]

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New post 15 Jul 2018, 06:50
1
Viserion99 wrote:
A certain shop only sells items for a whole number of dollars and ninety-nine cents. If Mrs. Jones spent less than $50 at the shop, how many items did she buy?

(1) She paid $36.72 for the items that she bought.
(2) Mrs. Jones did not spend more than $10.99 for any one item.


Price tag type:-whole number of $(1+0.99)$=$2
Total spent < $50
# of item=?

St1:- She paid $36.72 for the items that she bought.
It provided us the exact amount spent.
So, we can definitely determine the # of items. We needn't to compute. (#of items=Total paid/$2)
Sufficient.

St2:- Since amount spent on any one item is a variable, hence the #of items against these amount spent would be different .
Hence, total no of items would be different in different cases.
Insufficient.

Ans. (A)
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Re: A certain shop only sells items for a whole number of dollars and nine  [#permalink]

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New post 18 Jul 2018, 10:17
1
1
Let 'x' be the amount paid as whole number of dollars and 'y' be the number of items, each worth 99 cents.
Then, we have
x + (0.99)*y < 50

Statement 1:
x + (0.99)*y = 36.72
Now we need to find y such that (0.99)*y results in number with 0.72 being the decimal part. The only number which when multiplied by 9 gives unit digit as 2 is 8. Hence, we will try with y as 8, 18 and 28. Only 28 fits in since
(1 - .01)*28 = 27.72. Thus, we've a unique solution.

Statement 2:
Since exact cost may vary, it is insufficient.

Answer is (A)
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Re: A certain shop only sells items for a whole number of dollars and nine  [#permalink]

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New post 18 Jul 2018, 11:19
This is difficult can someone provide a detailed explanation
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A certain shop only sells items for a whole number of dollars and nine  [#permalink]

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New post 06 Sep 2018, 07:04
Viserion99 wrote:
A certain shop only sells items for a whole number of dollars and ninety-nine cents. If Mrs. Jones spent less than $50 at the shop, how many items did she buy?

(1) She paid $36.72 for the items that she bought.

(2) Mrs. Jones did not spend more than $10.99 for any one item.


Can someone please explain the solution?
The question itself took me so long to understand.
Would one prefer to skip these kind of questions or spend more than 2 minutes trying to solve it?


(1) She paid $36.72 for the items that she bought.
The decimal ends with 2 & price of all the items are of the form x.99
based on unit digits rule 9*8=72 (ends in a 2)
so Jones must have purchased 8 or 18 or 28 items. but we can come up with a exact number if we calculate.


(2) Mrs. Jones did not spend more than $10.99 for any one item.
This statement does not give any information to help decide the no. of items purchased

OA A.
Kindly correct me if my explanation is incorrect.
Thanks in advance.
Intern
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A certain shop only sells items for a whole number of dollars and nine  [#permalink]

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New post 18 Sep 2018, 21:53
I guess I got something wrong, cause I also found that y is equal to 28, which gives us $27,72. However we are left with remaining $9 (36.72-27.79), and since we are not told the exact price of items, what if she purchased 9 items, each for $1 or just one item for $9? Thus, I got answer E. Please help me understand what is wrong.
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Re: A certain shop only sells items for a whole number of dollars and nine  [#permalink]

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New post 19 Sep 2018, 09:32
OA is A. Here is my understanding.

For (1). She paid $36.72 . Since prices of all items cab be 0.99 , 1.99 , 2.99 .... Here we see that each one of them is $0.01 from whole number. Also since 37-36.72 = 0.28. So she must have bought 28 items only.

For (2) , nothing can be accurately said.
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Re: A certain shop only sells items for a whole number of dollars and nine   [#permalink] 19 Sep 2018, 09:32
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