What is the total number of coins that Bert and Claire have?

SOLUTION

What is the total number of coins that Bert and Claire have?

Question: \(B+C=?\)

(1) Bert has 50 percent more coins than Claire --> \(B=1.5C\). Not sufficient.

(2) The total number of coins that Bert and Claire have is between 21 and 28 --> \(21<B+C<28\). Not sufficient.

(1)+(2) From (1) we have \(B=1.5C\) and from (2) we have \(21<B+C<28\), leading to \(21<1.5C+C<28\) --> \(21<2.5C<28\). Three values of C satisfy this inequality: 9, 10, and 11. However, for 9 and 11, the value of B from \(B=1.5C\) won't be an integer. Therefore, C can only be 10 --> \(B=1.5C=15\) --> \(B+C=25\). Sufficient.

Answer: C.
_________________

1) Let of no of coins with Claire = 2x
Let of no of coins with Bert = 3x
2x+3x = 5x --->x can take any value - Insufficient

2) No of coins can take any integer value from 21 to 28- Insufficient

1+2) Total no of coins must be a multiple of 5 & between 21 & 28. Only possible integer value is 25--->Sufficient
Answer C

let the total number of coins be t.
Stamnt A: B = 1.5C --> not sufficient
Statment B: 21<B+C <28

usinng both:
T = B+C = c+1.5c =2.5c
now: anythig between 21 and 28 which is a multiple of 2.5 is 22.5/25/27.5

Since coins cannot be in decimal points , we are left with only one option that is t=25.
thus, OA: C
using both A and B together


Whats the OA?

We need to find out B + C

statement 1

B=0.5C+C

insufficient can't get a value

statement 2

21<B+C<28 again no value insufficient

combining 1 and 2

21<1.5C+C<28
21<2.5C<28 ( multiply by 2)
42<5C<56

so now the values for 5c are the multiples between 42 and 56 so we have 3 values

5C=45 >>> C=9
5C=50 >>> C=10
5C=55 >>> C=11

but we need to satisfy the condition that B=1.5C this is only possible when C = 10 since we need an integer value so 11 and 9 are ruled out

B+C=10+15=25

So the answer is C.

If Bert has B coins and Claire has C coins. Then total number of coins =B+C

From Statement 1
B =1.5 C or B/C=3/2
Ratio of B and C is 3:2 => Only inference from this we can make is, total number must be a multiple of 5.
Not sufficient

From statement 2
21<=B+C<=28
Multiple values for B+C - not sufficient

Combining the information from statement 1 and 2.
Total number of coins = 25

Hence C.

Hi All,

On Test Day, you're going to face a few questions in the Quant section that are perfect for "brute force" - you don't have to be a genius to get the correct answer and you don't need to have any specialized knowledge either. You DO have to put pen to pad and do some basic work though.

Here, we're asked for the total number of coins that Bert and Clair have.

Fact 1: Bert has 50 percent more coins than Claire.

Since you can't have a "fraction" of a coin, this piece of information provides just a little bit of info about the relationship between the number of coins that Bert has and the number of coins that Claire has.

IF.....
Claire has 1 coin, Bert has 1.5 coins, which does NOT make sense (he can't have half a coin).
Claire has 2 coins, then Bert has 3 coins. THIS makes sense. The total is 5 coins.
Claire has 4 coins, then bert has 6 coins. This also makes sense. The total is 10 coins.
Fact 1 is INSUFFICIENT.

You may have noticed that the total number of coins is going to be a multiple of 5. You don't need to know that to answer the question (although it would likely save you some time later on).

Fact 2: The total number of coins that Bert and Claire have is between 21 and 28.

This gives us more direct information, but no exact value.
Fact 2 is INSUFFICIENT.

Combined, we know....
Bert has 50 percent more coins than Claire.
The total number of coins that Bert and Claire have is between 21 and 28.

From here, you can "map out" the possibilities....
We already know that Claire MUST have an EVEN number of coins....so let's start there....

IF...
Claire = 6, then Bert = 9 and the total is 15. This does not fit the given range, so it can't be the answer.
Claire = 8, then Bert = 12 and the total is 20. This does not fit the given range, so it can't be the answer.
Claire = 10, then Bert = 15 and the total is 25. This DOES fit the given range, so it COULD be the answer.
Claire = 12, then Bert = 18 and the total is 30. This does not fit the given range, so it can't be the answer.

As the number of coins Claire has increases, then the total will increase (and continue to be out of the given range). This means that there's JUST ONE answer that fits all of the given information.
Combined, SUFFICIENT.

Final Answer:

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

I tried the estimation strategy and I have 2 possible solutions that match the criterion. If they have 16 and 8 coins or they have 18 and 9 coins. Need help understanding the same.

It says that Bert has 50 percent more coins than Claire (B = 1.5C), not twice as many (B = 2C). Please refer to the solutions above.
_________________

Solution:

Question Stem Analysis:

We need to determine the total number of coins Bert and Claire have.

Statement One Alone:

Statement one alone is not sufficient to answer the question. For example, if Claire has 2 coins, then Bert has 2 x 1.5 = 3 coins, and hence they have 2 + 3 = 5 coins together. However, if Claire has 4 coins, then Bert has 4 x 1.5 = 6 coins, and hence they have 4 + 6 = 10 together.

Statement Two Alone:

Statement two alone is not sufficient to answer the question since the total number of coins they have could be any integer value from 22 to 27, inclusive.

Statements One and Two Together:

From statement one, if we let c be the number of coins Claire has, then the number of coins Bert has is 1.5c and the total number of coins they have is c + 1.5c = 2.5c = 5c/2. From statement two we see that the total number of coins is an integer value from 22 to 27, inclusive. If we let this value be T, we can create the equation:

5c/2 = T

c = T * 2/5 = 2T/5

Since c is an integer and 2 is not divisible by 5, we see that T must be divisible by 5. From the integers 22 to 27, we see that only 25 is divisible by 5. Therefore, T must be 25. That is, the total number of coins Bert and Claire have is 25.

Answer: C
_________________

Answer: Option C

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Determine the total number of coins Bert and
Claire have. If B represents the number of coins
that Bert has and C represents the number of
coins that Claire has, determine B + C.
(1) Bert has 50% more coins than Claire, so
B = l.5C, and B+ C =l.5C + C = 2.5C, but
the value of Ccan vary; NOT sufficient.
(2) The total number of coins Bert and
Claire have is between 21 and 28, so
21 < B+ C < 28 and, therefore, B + C could
be 22, 23, 24, 25, 26, or 27; NOT sufficient.
Taking (1) and (2) together, 21 < 2.5C < 28 and
then 11 < C < 11 or 8.4 < C < 11.2.

If C =9, then B =(1.5)(9) = 13.5; if C =10,
then B =(1.5)(10) = 15; and if C =11, then
B =(1.5)(11) =16.5. Since B represents a number
of coins, Bis an integer.Therefore, B=15, C=10,
and B+ C=25.

Let b = bert's coins and c = claire's coins

(1) b = 1.50c -- not sufficient
(2) 21 ≤ b + c ≤ 28 -- not sufficient

(1) & (2) 1.50c + c = 2.5c
2.5c = some integer
only 25 fits the criteria, so 2.5c = 25

Answer is C.

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