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

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What is the total number of coins that Bert and Claire have? [#permalink] New post 15 Oct 2012, 03:53
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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.

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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 15 Oct 2012, 03:53
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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) Since from (1) B=1.5C and from (2) 21<B+C<28, then 21<1.5C+C<28 --> 21<2.5C<28. Three values of C satsify this inequality; 9, 10, and 11. But for 9 and 11, the value of B from B=1.5C. won't be an integer, thus C can only be 10 --> B=1.5C=15 --> B+C=25. Sufficient.

Answer: C.
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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 15 Oct 2012, 03:59
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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
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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 15 Oct 2012, 05:39
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Bunuel 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.



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?
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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 15 Oct 2012, 08:44
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1) Bert can have 10, Claire can have 15 OR Bert can have 20, Claire can have 30. Not sufficient.
2) Clearly not sufficient

Both together

1.5 B + B = 2.5 B= x.

The only number in the range to give an integer value for B is 25.

So, answer is C
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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 16 Oct 2012, 04:47
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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.
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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 16 Oct 2012, 05:04
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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.
Bunuel 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.

Practice Questions
Question: 65
Page: 280
Difficulty: 600

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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 19 Oct 2012, 04:46
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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) Since from (1) B=1.5C and from (2) 21<B+C<28, then 21<1.5C+C<28 --> 21<2.5C<28. Three values of C satsify this inequality; 9, 10, and 11. But for 9 and 11, the value of B from B=1.5C. won't be an integer, thus C can only be 10 --> B=1.5C=15 --> B+C=25. Sufficient.

Answer: C.

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 25 Nov 2013, 10:18
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Re: What is the total number of coins that Bert and Claire have? [#permalink] New post 10 Jan 2014, 07:51
Bunuel 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.

Practice Questions
Question: 65
Page: 280
Difficulty: 600


The stem asks us: B + C = TC, what is TC?

1) This tells us that B = 1.5 C, so now we have two unknowns: 2.5C = TC, insufficient
2) Gives us a range of possible values, so in itself 2 is insufficient because the value could be any of 6 values. Insufficient

1 + 2 : Look closely: given our equation from 1, TC must be a multiple of 5 (we cannot have fractions of coins), and given the restriction in 2, we only have ONE possible multiple of 5: 25...

So, TC = 25... Answer is C.
Re: What is the total number of coins that Bert and Claire have?   [#permalink] 10 Jan 2014, 07:51
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