If b is prime and the symbol # represents one of the following operati

Question

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

GMATinsight · Answer

Question : is the value of b # 2 even or odd?

Statement 1:  (b # 1) # 2 = 5

The only possibility here is   (2 + 1) + 2 = 5

# can't be Subtraction as ((b - 1)-2) = 5 will make b = 8 which is not Prime
# can't be Multiplication as b *1*2 = 5 will make b = 5/2 which is not Prime
# can't be Division as (b /1)/2 = 5 will make b = 10 which is not Prime

SUFFICIENT

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

One of the possibilities is  4 + b = 3 + (1 + b)  with # equivalent to Addition

BUT # can be Subtraction as well because, 4 - b = 3 - (1 - b) will make b = 2, which is Prime Number

But Since b can be only 2 therefore b#2 will always be even.

SUFFICIENT

Answer: option D

lipsi18 · Answer

B#2 =E or O
1. Only value possible will be + =# ; 2+2+1=5; hence b#2 =E ; sufficient
2. Even value of b will be 2 , 4+2=3+1+2 ; therefore b#2 =E; but 4-2=2,3-(1-2)=4, hence only one value possible +; sufficient

Hence answer is D
Thanks,

Vaibhav21 · Answer

(1) (b # 1) # 2 = 5
only value for b here is 2 and only operation used = addition to get 5
suff
(2) 4 # b = 3 # (1 # b) and b is even
value of b= 2 operations = addition
Hence Suff
Answer D

TheNightKing · Answer

Given:
b is Prime.
# can be +,-,/, or *.

Ask: b#2 is even or odd. All you need is to figure out what is # and value of b.

Statement 1:
(1) (b # 1) # 2 = 5
Lets try b=2
(2 + 1) + 2 = 5 - Works
(2 - 1) - 2 = 5 - Nope
(2 / 1) / 2 = 5 - Nope
(2 * 1) * 2 = 5 - Nope

Try with b=3. Basically you should try an odd value too. None will work.

Sufficient. b=2 and # is "addition"

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

Good thing is b can only be 2.
4 + 2 = 3 + (1 + 2) - Works
4 - 2 = 3 - (1 - 2) - Nope
4 / 2 = 3 / (1 / 2) - Nope
4 * 2 = 3 * (1 * 2) - Nope

So b is 2 and # is addition.
Sufficient

Hence D.

bumpbot · Answer

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If b is prime and the symbol # represents one of the following operati

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