The average of a, b and c is 11, where a, b , c are positive integers.

Question

The average of a, b and c is 11, where a, b , c are positive integers. If c is two greater than a, which of the following must be true?

I. a is even
II. b is odd
III. c is odd

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III

KSBGC · Answer

a + b + c = 33

Given,

c = a + 2

Then ,

a + b + c = 33

a + b + a + 2 = 33

2a + b = 31.

2a = even.

b = odd.

B is the correct answer.

Archit3110 · Answer

given
a+b+c=33
and c=2+a
so
2a+b=31
out of given options; b has to be odd and a is even
e+o+e=odd

a could be even or odd irrespective 2*a = even so b has to be odd 
now 
a+b+c=33
we can have two cases whatever a is shall be same for c i.e if a is odd then c will also be odd and if its even then c will be even as c=a+2

so
case 1 ; a=c = even
even+odd+even = odd true
case 2; a=c=odd
odd+odd+odd=odd true

what we get as must true in both cases is b = odd
IMO B

CareerGeek · Answer

Hey  Archit3110

2 cases are possible odd + odd + odd
= odd
Or 
Even + odd + even = odd

And c and a are either both even or odd as c = a + 2

So, I guess it’s only B.

Posted from my mobile device

ScottTargetTestPrep · Answer

Since the average of a, b, and c is 11, the sum of a, b, and c is 33. Since c is 2 greater than a, we have:

a + b + a + 2 = 33

2a + b = 31

Since 2a is even, we see that b must be odd. However, a could be odd or even. Since c is 2 greater than a, c has the same parity as a. So c could be odd or even also.

Answer: B

saukrit · Answer

If b is even then the sum a+b+c can never be odd ..Why? Because c=a+2(given) . Hence a and c can either be both even or both odd, and in both cases sum of a and c will be even. SO for the sum a+b+c to be odd b has to be odd.  Hence Correct answer is B

AyushCrackVerbal · Answer

Concept:

Even + Even = Even

Even + Odd = Odd

Odd + Even = Odd

Odd + Odd = Even

As per the question:

\frac{a + b + c}{3}  = 11

a + b + c = 33  .......  Equation A

c = 2 + a

Substituting the value of "c" in  Equation A :

a + b + 2 + a = 33

2a + b = 33

2a is even irrespective of a being odd or even. For 2a + b to be odd, b must be odd. Therefore Statement II is true.

Since a can be odd as well as even, statement I is not always true.

To check for c:

a + b + c = 33

We know that b is odd. For a + b + c to be odd, a + b must be even.

a + b will be even when:

1) a is even ; b is even
2) a is odd ; b is odd

Since a can be even as well as odd, b also can be even as well odd respectively. Hence statement III is not always true.

The correct answer is  B

The average of a, b and c is 11, where a, b , c are positive integers.

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The average of a, b and c is 11, where a, b , c are positive integers.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards