Data Sufficiency

Mo2men wrote:Anthony can purchase bagels at $1.99 for a specialty bagel and $15.99 for a package of one dozen plain bagels. If Anthony can purchase only specialty bagels or packages of plain bagels, did Anthony purchase any plain bagels?

(1) Anthony spent less than $32.00
(2) Anthony spent more than $31.90

Source: Veritas

OA: C

Hi Mo2men,

We are given that the price of a specialty bagel = $1.99 and the price of 12 plain bagels = $15.99

Let us see each statement one by one.

S1: Anthony spent less than $32.00.

You may test a couple of extreme values.

If Anthony bought only few specialty bagels, the answer is NO.
If Anthony bought only two packages of plain bagels, the answer is YES. Insufficient.

S2: Anthony spent more than $31.90.

As with statement 1, statement 2 is also not sufficient.

S1 & S2:

We have: 31.90 < AMOUNT < 32.00

Let's test some values, assuming that Anthony did not buy a package of plain bagels.

We have the price of a specialty bagel = $1.99. Let's take it $2 for the time being. So, if he buys 16 specialty bagels, the amount < $32. Since '31.90 < AMOUNT < 32.00' is too close, we must get the value of actual amount, which is 1.99*16 = $31.84. Since 31.84 < the MINIMUM sum Anthony spent (31.90), he must not have bought 16 specialty bagels.

Let's see if he bought 17 specialty bagels. The amount would be 31.84 + 1.99 = 32.83. This is also not possible since 32.83 > the MAXIMUM amount Anthony spent (32).

This implies that Anthony must have bought at least one package of plain bagels. Sufficient.

C[/quote]

He may do the following.

1. Buy one dozen plain + 8 specialty bagels: Amount = 15.99 + 8*1.99 = $31.91.

OR

2. Buy two dozen plain bagels: Amount = 2*15.99 = $31.98.

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Hyderabad | Mexico City | Toronto | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Hi Mo2men,

This question ultimately comes down to 'limited options' and whether they actually exist or not with the given information. In real basic terms, this question can be re-written as "Are there any '15.99s' in the group?" This is a YES/NO question.

1) Anthony spent less than $32.00

There could be one or two 15.99s in the group, in which case the answer would be YES
There might not be a 15.99 in the group, in which case the answer would be NO
Fact 1 is INSUFFICIENT

2) Anthony spent more than $31.90

There could be one or more 15.99s in the group, in which case the answer would be YES
There might not be a 15.99 in the group, in which case the answer would be NO
Fact 2 is INSUFFICIENT

Combined, we have a very narrow "window" ($31.90 < TOTAL < $32.00).

IF....there were two $15.99s, then the total would be $31.98 and the answer to the question would be YES
IF....there was one $15.99 and eight $1.99s, then the total would be $31.91 and the answer to the question would be YES
IF... there were NO $15.99s, then we would have just $1.99s; however - with 16 of them we have a total of $31.84 and with 17 of them we have a total of $33.83. Thus, there is NO WAY to get into the given range if we have zero $15.99s, so there isn't a NO answer under these circumstances. Thus, the answer to the question is ALWAYS YES.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich