If a and b are single digits from 0 to 9, inclusive, what is the value

Question

If a and b are single digits from 0 to 9, inclusive, what is the value of (a + b)?

(1) The number 25a7b is divisible by 36.
(2) The number a1b is divisible by 4.

Luckisnoexcuse · Answer

(1) 
36*2 = 72
only when b = 2 we can get 7 in the tenth digit
36*702 = 25272
36*712 = 25632 nope
36*722 = 25992 nope
36*692 = 24912 nope
hence a+b = 4

Sufficient

(2) a1b is divisible by 4
b can take 2, 6
a can take 1-9
Not sufficient
 
A

mohshu · Answer

luks like E to me....
here are my 2 cents....
if the number is divisible by 36,,it shud be divisible by both 9 and 4
for a number to b divisible by 9,, the sum if digits shud be divisible by 9
for a nummber to b divisible by 4 the last two digits shud be divisible by 4

stat 1: 25776,, a+b = 13
 25272 ,,a+b = 4
not suff

stat 2: b can be 2 or 6

both combined two diff ans,,
ans E

rulingbear · Answer

IMO, it helps to start from statement 2 as it's much simpler and may give hints to evaluate statement 1 
 Statement 2 is insufficient  using the divisibility rule by 4 i.e  b  is either 2 or 6 and  a  could be any number.

Evaluating statement 1:
From statement 2 we know that b is either 2 or 6 since it's divisible by 25a7b is divisible by 36,

Now combining the divisibility by 4 and 9 to find divisibility by 36, b is inconclusive as 72 and 76 are divisible by 4
Also by extension,  a  has dual values (2 and 7) that make 2+a+5+7+2 = 18 or 2+a+5+7+6 = 27 divisible by 9

Thus, statement 1 is also insufficient and the answer is E.

mohshu · Answer

in the number 25776, the last two digits are 76,,, and the number is very much divisible by 36...

rulingbear · Answer

Hi Monshu,

You are clearly right, missed that.

Devbek · Answer

The answer should be E.
Both statements combined you will have two cases:
b=2
and 
b=6

K_Leon · Answer

You are forgetting 25776
(1) Divisible by 36 means divisible by 4 and 9.
divisible by 4 means 7b divisible by 4 --> b=2 or 6
divisible by 9 means 2+5+7+a+b divisible by 9 but b can only take 2 or 6
with b=2 --> 16+a divisible by 9 --> a=2
with b=6 --> 20+a divisible by 9 --> a=7
(2) same info

E

bumpbot · Answer

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If a and b are single digits from 0 to 9, inclusive, what is the value

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