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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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Status: GMAT on july 13.
Joined: 10 Feb 2017
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GMAT 1: 650 Q48 V30
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
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Difficulty:

  95% (hard)

Question Stats:

29% (02:08) correct 71% (02:08) wrong based on 48 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
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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Regards,

PKN

Rise above the storm, you will find the sunshine

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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
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
Re: A certain shop only sells items for a whole number of dollars and nine &nbs [#permalink] 18 Jul 2018, 11:19
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