Data Sufficiency

Both the questions in OG 13 are similar but the solutions are different why?


Joanna bought only $0.15 stamps and $0.29 stamps.
How many $0.15 stamps did she buy?
(1) She bought $4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps
and $0.29 stamps.

Each gift certificate sold yesterday by a certain
bookstore cost either $10 or $50. If yesterday the
bookstore sold more than 5 gift certificates that cost
$50 each, what was the total number of gift
certificates sold yesterday by the bookstore?
(1) Yesterday the bookstore sold fewer than 10 gift
certificates that cost $10 each.
(2) The total cost of gift certificates sold yesterday
bythe bookstore was $460.[/b][/size]

Joanna bought only $0.15 stamps and $0.29 stamps.
How many $0.15 stamps did she buy?

(1) She bought $4.40 worth of stamps.

(2) She bought an equal number of $0.15 stamps
and $0.29 stamps.

It is important to note how a problem is RESTRICTED.
This problem is restricted to POSITIVE INTEGERS: Joanna cannot by 1/2 of a stamp or -2 stamps.

Statement 1: 15x + 29y = 440.
When a problem is restricted to positive integers, BE SUSPICIOUS: quite often 1 linear equation with 2 variables will provide sufficient information to determine the value of each variable.
Here, we need to determine whether more than one combination of positive integers will satisfy the equation 15x + 29y = 440.

Rephrasing the equation, we get:
29y = 440 - 15x = (multiple of 5) - (multiple 5) = multiple of 5.

Since 29y must be a multiple of 5, there are only 3 options:
Case 1: 5*29 = 145.
Case 2: 10*29 = 290.
Case 3: 15*29 = 435.

In each case, the amount remaining must be a MULTIPLE OF 15:
Case 1: 440-145=295, which is not a multiple of 15.
Case 2: 440-290=150, which is a multiple of 15.
Case 3: 440-435=5, which is not a multiple of 15.

Since only ONE CASE is viable, SUFFICIENT.

Statement 2: She bought an equal number of $0.15 stamps and $0.29 stamps.
No way to determine how many 15-cent stamps were purchased.
INSUFFICIENT.

The correct answer is A.

A savvy test-taker -- one familiar with how DS problems are written and structured -- could take the following approach:

Clearly, the two statements combined provide sufficient information to determine how many 15-cent stamps were purchased.
Eliminate E.

Clearly, statement 2 does not by itself provide sufficient information.
If all we know is that Joanna purchased an equal number of each type of stamp, she could have purchased 1 of each type, 2 of each type, 3 of each type, etc.
Eliminate B and D.

The correct answer must be C or A.
The relationships described by the two statements are extremely straightforward.
If the OA here is C, then virtually EVERYONE will answer the question correctly, rendering the question pretty much useless.

Thus, the correct answer almost certainly is A.

[email protected] wrote: Each gift certificate sold yesterday by a certain
bookstore cost either $10 or $50. If yesterday the
bookstore sold more than 5 gift certificates that cost
$50 each, what was the total number of gift
certificates sold yesterday by the bookstore?

1) Yesterday the bookstore sold fewer than 10 gift
certificates that cost $10 each.
(2) The total cost of gift certificates sold yesterday
by the bookstore was $460.

It is important to note not only how a problem is restricted but also how it ISN'T.
In the first problem, one of the prices is an unusual prime number (29), while the total cost is an unusual multiple of 5 (435), greatly restricting the number of possible solutions.
Here, the prices (10 and 50) and the total cost (460) are all multiples of 10.
Thus, we should suspect that SEVERAL solutions might be viable.

According to the question stem, the revenue from the $50 gift certificates can be ANY MULTIPLE OF 50 GREATER THAN 250:
300, 350, 400, 450...
Statement 1 indicates that the revenue from the $10 gift certificates can be ANY MULTIPLE OF 10 LESS THAN 100:
90, 80, 70, 60, 50, 40, 30, 20, 10, 0.
Statement 2 indicates that the SUM = 460.

Case 1: 400 + 60 = 460.
Case 2: 450 + 10 = 460.
Since more than one combination works, the two statements combined are INSUFFICIENT.

The correct answer is E.
[spoiler][/spoiler]