If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

b # 2 = 2+2 = 4(Even) - Sufficient!

2) 4 # b = 3 # (1 # b) and b is even
Only even prime number is 2.

b # 2 = 2+2 = 4(Even) - Sufficient!

IMO D

gmatblood wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5
2) 4 # b = 3 # (1 # b) and b is even

D it is!

1) almost immediately knew only value of b would be 2 and # is addition.
2) b is even meant leave the rest and the answer would be even !

A is not the answer because for addition, sub and multiplication B#2 is even and for division B =10 and B/2 = 5 odd. We cannot judge B#2 based on 1st option

B+2 = 4; B-2 = 6; B/2 = 5.. even even odd.. A is bad

The tough thing is that 1 and 2 options have paranthesis too.. these take precedence as well..

neelgandham wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

b # 2 = 2+2 = 4(Even) - Sufficient!

2) 4 # b = 3 # (1 # b) and b is even
Only even prime number is 2.

b # 2 = 2+2 = 4(Even) - Sufficient!

IMO D

HSPA wrote:A is not the answer because for addition, sub and multiplication B#2 is even and for division B =10 and B/2 = 5 odd. We cannot judge B#2 based on 1st option

The tough thing is that 1 and 2 options have paranthesis too.. these take precedence as well..

neelgandham wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

b # 2 = 2+2 = 4(Even) - Sufficient!

2) 4 # b = 3 # (1 # b) and b is even
Only even prime number is 2.

b # 2 = 2+2 = 4(Even) - Sufficient!

IMO D

I am afraid you got the question wrong, the question can be rephrased to. What is # and what is the value of B? From the 1st statement we found that # = + and B = 2

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

No other sign or No other value satisfies the equation.

Okay I missed that B is prime.. sorry for the confusion..

neelgandham wrote:

HSPA wrote:A is not the answer because for addition, sub and multiplication B#2 is even and for division B =10 and B/2 = 5 odd. We cannot judge B#2 based on 1st option

The tough thing is that 1 and 2 options have paranthesis too.. these take precedence as well..

neelgandham wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

b # 2 = 2+2 = 4(Even) - Sufficient!

2) 4 # b = 3 # (1 # b) and b is even
Only even prime number is 2.

b # 2 = 2+2 = 4(Even) - Sufficient!

IMO D

I am afraid you got the question wrong, the question can be rephrased to. What is # and what is the value of B? From the 1st statement we found that # = + and B = 2

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

No other sign or No other value satisfies the equation.

neelgandham wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

b # 2 = 2+2 = 4(Even) - Sufficient!

2) 4 # b = 3 # (1 # b) and b is even
Only even prime number is 2.

b # 2 = 2+2 = 4(Even) - Sufficient!

IMO D

Based on 1) you can prove that "#" represents addition and that b is 2.

I don't think you can do that with based on equation 2. As per equation 2, "#" can represent either subtraction or addition. And also because b is even, b must be 2. So b#2 could either be 4 or 0. INSUFFICIENT. So IMO A

What is the OA?

Option 2 says that B is prime and B is even.. there is only one value that B can be = 2

2 is the only even prime number... HTH

Gokhra wrote:

neelgandham wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

b # 2 = 2+2 = 4(Even) - Sufficient!

2) 4 # b = 3 # (1 # b) and b is even
Only even prime number is 2.

b # 2 = 2+2 = 4(Even) - Sufficient!

IMO D

Based on 1) you can prove that "#" represents addition and that b is 2.

I don't think you can do that with based on equation 2. As per equation 2, "#" can represent either subtraction or addition. And also because b is even, b must be 2. So b#2 could either be 4 or 0. INSUFFICIENT. So IMO A

What is the OA?

HSPA wrote:Option 2 says that B is prime and B is even.. there is only one value that B can be = 2

2 is the only even prime number... HTH

Gokhra wrote:

neelgandham wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5

# = + ; b+3=5; b=2.(Prime)
# = - ; b-3=5; b=8.(Non Prime)
# = * ; b*2=5; b!=Integer.(Non Prime)
# = % ; b%2=5; b=10(Non Prime)

b # 2 = 2+2 = 4(Even) - Sufficient!

2) 4 # b = 3 # (1 # b) and b is even
Only even prime number is 2.

b # 2 = 2+2 = 4(Even) - Sufficient!

IMO D

Based on 1) you can prove that "#" represents addition and that b is 2.

I don't think you can do that with based on equation 2. As per equation 2, "#" can represent either subtraction or addition. And also because b is even, b must be 2. So b#2 could either be 4 or 0. INSUFFICIENT. So IMO A

What is the OA?

Agreed, but the question doesn't ask about b, it asks about b#2. Without knowing what "#" represents, how can we answer whether b#2 is even or odd?

gmatblood wrote:If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?

1) (b # 1) # 2 = 5
2) 4 # b = 3 # (1 # b) and b is even

A very logical thing we should do here is NOT to check for different Mathematical expressions other than MULTIPLY. (the only exception here is b= 2, which can be quickly checked)

Can someone tell me why I said so? That logic will make this question very easy.

Gokhra wrote: Agreed, but the question doesn't ask about b, it asks about b#2. Without knowing what "#" represents, how can we answer whether b#2 is even or odd?

Good question. Well if you know b is 2 then the next best thing to do is put that value in the given expression [4 # b = 3 # (1 # b].

This way you will be able to find what is #. But, I like your question. the explanation provided by other poster does not include that part. For example if # is DIVIDE then 2/2 = 1 [ which is NOT even]

saketk wrote:

Gokhra wrote: Agreed, but the question doesn't ask about b, it asks about b#2. Without knowing what "#" represents, how can we answer whether b#2 is even or odd?

Good question. Well if you know b is 2 then the next best thing to do is put that value in the given expression [4 # b = 3 # (1 # b].

This way you will be able to find what is #. But, I like your question. the explanation provided by other poster does not include that part. For example if # is DIVIDE then 2/2 = 1 [ which is NOT even]

Well this is my third post in this thread..

I missed your penultimate post.

ZERO is in-fact EVEN.

An integer n is called *even* if there exists
an integer m such that n = 2m, and *odd* if n+1 is even. From this,
it is clear that 0 = (2)(0) is even.

So, the second statement is also sufficient.