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Math Expert V
Joined: 02 Aug 2009
Posts: 7960
If a+b+c=62, what is the value of a?  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 48% (01:50) correct 52% (01:54) wrong based on 218 sessions

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If a+b+c=62, what is the value of a?

1) a=2c
2) There is one integer between c and b, and c and b are integers .

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Intern  Joined: 11 Oct 2015
Posts: 9
GMAT 1: 600 Q44 V28 Re: If a+b+c=62, what is the value of a?  [#permalink]

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St 1: insufficient as we dont know the value of B

St 2: insufficient as we dont know about A

combining

a = 2c
a+b+c = 62
3c + b = 62
as one number is between b and c and b and c are integers and the values which satisfies 3c + b= 62 is 15 and 17
by this we can find the value of a which is 30(2*15)

so it is C
Marshall & McDonough Moderator D
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Re: If a+b+c=62, what is the value of a?  [#permalink]

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1
2
a+b+c=62, a = ?

St1: a = 2c --> Clearly insufficient as we do not know the value of b

St2: There is one integer between c and b, and c and b are integers
Assuming that there is exactly one consecutive integer value between c and b,
b = c + 2 --> a + 2c = 60
or
c = b + 2 --> b = c - 2 --> a + 2c = 64
Also, a + b + c = 62
St2 is insufficient to determine the value of a

Combining both the statements,
a = 2c. So there are 2 possibilities.
4c = 60 --> c = 15, a = 30 and b = 17
or
4c = 64 --> c = 16, a = 32 and b = 14.
We still do not have a unique solution for a.

Math Expert V
Joined: 02 Aug 2009
Posts: 7960
Re: If a+b+c=62, what is the value of a?  [#permalink]

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Vyshak wrote:
a+b+c=62, a = ?

St1: a = 2c --> Clearly insufficient as we do not know the value of b

St2: There is one integer between c and b, and c and b are integers
Assuming that there is exactly one consecutive integer value between c and b,
b = c + 2 --> a + 2c = 60
or
c = b + 2 --> b = c - 2 --> a + 2c = 64
Also, a + b + c = 62
St2 is insufficient to determine the value of a

Combining both the statements,
a = 2c. So there are 2 possibilities.
4c = 60 --> c = 15, a = 30 and b = 17
or
4c = 64 --> c = 16, a = 32 and b = 14.
We still do not have a unique solution for a.

Hi,
Good one..+1 kudos
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GMAT 1: 760 Q51 V42 GPA: 3.82
If a+b+c=62, what is the value of a?  [#permalink]

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1
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a+b+c=62, what is the value of a?

1) a=2c
2) There is one integer between c and b, and c and b are integers.

There are 3 variables (a, b and c) and 1 equation (a+b+c=62) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Since the condition 1) and 2) each has 1 equation, there is high chance that C is going to be the answer. Using both the condition 1) and 2), we can see that the condition 1) states a=2c and the condition 2) states c=b+2 or b=c+2. From these conditions, we can get 2 values of a. The answer is not unique, and the conditions are not sufficient. Therefore, the correct answer is E.

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In the case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.
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GMAT 1: 580 Q41 V29 GMAT 2: 580 Q43 V27 Re: If a+b+c=62, what is the value of a?  [#permalink]

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sandeepch wrote:
St 1: insufficient as we dont know the value of B

St 2: insufficient as we dont know about A

combining

a = 2c
a+b+c = 62
3c + b = 62
as one number is between b and c and b and c are integers and the values which satisfies 3c + b= 62 is 15 and 17
by this we can find the value of a which is 30(2*15)

so it is C

Very nice try. but other possible combination is (32,14, 16). It took me 4 minutes to find other possible combination and a flaw in this method. Therefore, it is insufficient to solve the question.
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Re: If a+b+c=62, what is the value of a?  [#permalink]

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chetan2u wrote:
If a+b+c=62, what is the value of a?

1) a=2c
2) There is one integer between c and b, and c and b are integers .

We are given that a + b + c = 62 and need to determine the value of a.

Statement One Alone:

a=2c

Using the information in statement one, we have:

2c + b + c = 62

3c + b = 62

We see that we cannot determine a. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

There is one integer between c and b, and c and b are integers.

Using the information in statement one, we know that either c = b + 2 or b = c + 2. We cannot determine a. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we know that a = 2c and that either c = b + 2 or b = c + 2. However, since we cannot determine whether c = b + 2 or b = c + 2, we do not have enough information to determine a.

To illustrate, if c = b + 2, we have the following three equations:

1) c = b + 2

c - 2 = b

2) a = 2c

3) a + b + c = 62

Thus:

2c + c - 2 + c = 62

4c = 64

c = 16

Thus, a = 32.

However if b = c + 2, we have:

1) b = c + 2

2) a = 2c

3) a + b + c = 62

Thus:

2c + c + 2 + c = 62

4c = 60

c = 15

Thus, a = 30.

Since a can be either 30 or 32, we do not have enough information.

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Re: If a+b+c=62, what is the value of a?  [#permalink]

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_________________ Re: If a+b+c=62, what is the value of a?   [#permalink] 11 Aug 2018, 13:04
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