Anthony can purchase bagels at $1.99 for a specialty bagel

[Mo2men]

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

[Jay@ManhattanReview]

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
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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

[Matt@VeritasPrep]

I think we could put this pretty neatly as follows:

Let's say Anthony bought s specialty bagels and d packages of one dozen plain bagels. We want to know if d > 0.

S1:

1.99s + 15.99d < 32

There are a couple solutions here, such as s = 1, d = 0, or s = 1, d = 1. Since this gives conflicting results, S1 is insufficient.

S2:

31.90 < 1.99s + 15.99d

Same issue as above, we could have s = 1000, d = 0, or s = 1, d = 1000.

S1 + S2

31.90 < 1.99s + 15.99d < 32.00

We could certainly have s = 0, d = 2, so d > 0 is possible. Now we need to see if d = 0 is possible.

31.90 < 1.99s < 32.00

Since 2.00 * 16 = 32, the only s value that would be in range is s = 16. But 1.99 * 16 = 31.84! So Anthony CANNOT have bought only specialty bagels.

From this we find that d = 0 is impossible, so d > 0, and we're done.