Data Sufficiency

alex.gellatly wrote:What is the total number of coins that Bert and Claire have?
(1) Bert has 50 percent more coins than Claire.
(2) The total number of coins that Bert and Claire have is between 21 and 28.

OK, I got the correct answer by picking numbers and kind of guessing. Can someone show me a good algebraic approach?

Thanks!

Let us assume that the no. of coins that Bert has = B, and
no. of coins that Claire has = C
We have to find the value of B + C.

(1) Bert has 50% more coins than Claire implies B = C + 0.50C or B = 1.5C
So, B + C = 1.5C + C = 2.5C, but we do not know the value of C; NOT sufficient.

(2) The total number of coins that Bert and Claire have is between 21 and 28 implies 21 < (B + C) < 28.
This means B + C can be 22, 23, 24, 25, 26, or 27. But there is no unique value; NOT sufficient.

Combining (1) and (2), B + C = 2.5C and 21 < (B + C) < 28
21 < 2.5C < 28
21/2.5 < C < 28/2.5
8.4 < C < 11.2 implies C can be 9 or 10.

When C = 9, B = 1.5C = 1.5 * 9 = 13.5, which is not possible as B is the no. of coins that Bert has, which should be an integer.
When C = 10, B = 1.5C = 1.5 * 10 = 15. Here B + C = 15 + 10 = 25; SUFFICIENT.

The correct answer is C.

alex.gellatly wrote:What is the total number of coins that Bert and Claire have?
(1) Bert has 50 percent more coins than Claire.
(2) The total number of coins that Bert and Claire have is between 21 and 28.

We need to determine the total number of coins that Bert and Claire have. Let's define two variables.

b = the number of coins that Bert has

c = the number of coins that Claire has

Thus, we know that b + c = total number of coins Bert and Claire have.

Statement One Alone:

Bert has 50 percent more coins than Claire.

From the information in statement one we can create the following equation:

b = 1.5c

Without knowing b or c, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The total number of coins that Bert and Claire have is between 21 and 28.

From statement two we know that 21 < b + c < 28. However, we cannot determine the value of b + c, so statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that b = 1.5c and 21 < b + c < 28.

Since b = 1.5c, we can substitute 1.5c for b in the inequality 21 < b + c < 28.

21 < 1.5c + c < 28

21 < 2.5c < 28

21/2.5 < c < 28/2.5

210/25 < c < 280/25

8 2/5 < c < 11 1/5

Because c must be an integer, we know that 9 ≤ c ≤ 11. Thus c could equal 9, 10, or 11.

However, because both b and c must be integers, the only value for c that will make b an integer in the equation b = 1.5c, is c = 10.

Thus, b = 1.5 x 10 = 15 and b + c = 15 + 10 = 25. Statements one and two together are sufficient to answer the question.

Answer: C