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# For all numbers a and b, the operation # is defined by a # b = 2a + 2b

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Re: For all numbers a and b, the operation # is defined by a # b = 2a + 2b [#permalink]
Bunuel wrote:
For all numbers a and b, the operation # is defined by a # b = 2a + 2b + 1. What is the value of 6 # 1 ?

A. 6
B. 7
C. 13
D. 14
E. 15

Given; For all numbers a and b, the operation # is defined by a # b = 2a + 2b + 1.

Asked: What is the value of 6 # 1 ?

6 # 1 = 2*6 + 2*1 + 1 = 12 + 2 + 1 = 15

IMO E
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Re: For all numbers a and b, the operation # is defined by a # b = 2a + 2b [#permalink]
For all numbers a and b, the operation # is defined by a # b = 2a + 2b + 1. What is the value of 6 # 1 ?

A. 6
B. 7
C. 13
D. 14
E. 15--> correct

a # b = 2a + 2b + 1
6 # 1 = 2*6+2*1+1, as a=6 & b=1
6#1=15
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Re: For all numbers a and b, the operation # is defined by a # b = 2a + 2b [#permalink]
6#1= 2*6 + 2*1 +1 = 12+2+1 =15

Hence E
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Re: For all numbers a and b, the operation # is defined by a # b = 2a + 2b [#permalink]
Bunuel wrote:
For all numbers a and b, the operation # is defined by a # b = 2a + 2b + 1. What is the value of 6 # 1 ?

A. 6
B. 7
C. 13
D. 14
E. 15

6 # 1 = 2(6) +2(1) + 1 = 12 + 2 + 1 = 15

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Re: For all numbers a and b, the operation # is defined by a # b = 2a + 2b [#permalink]

Solution

Given:
• a # b = 2a + 2b + 1

To find:
• 6 # 1

Approach and Working Out:
• 6 # 1 = 2*6 + 2*1 + 1 = 12 + 2 + 1 = 15

Hence, the correct answer is Option E.

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Re: For all numbers a and b, the operation # is defined by a # b = 2a + 2b [#permalink]
Top Contributor
Very obvious that when we get such an easy question, we simply substitute the values and get the answer.

We can try an alternative approach. Now Even * Even or Even * Odd is always Even. Therefore 2a and 2b are Even.

Also, Even + Even = Even and Even + Odd = Odd. So 2a + 2b + 1 = even + even + odd = odd

Among the answer options A and D get eliminated. Now a = 6. 2a + 1 is 13 with taking he value of 2b.

The answer has to be greater than 13. Options B and C get eliminated.

Option E

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Re: For all numbers a and b, the operation # is defined by a # b = 2a + 2b [#permalink]