Data Sufficiency Quantitative

Is ab an even number ?
I. a is divisible by 3.
II. (b+1) is divisible by 4.
The correct answer it says is II, how??
If x^a = y^b > z^c, is x = y > z?
I. a = b > c
II. a = b = c
The answer is III, how??
If n is a natural number, is n ! < ^x ?
I. n is an even numbe...
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Statement 1 -
that is x+y<=20
(5+15=20 , 8+12=20..... )
so nothing can be said abt the value of x
Statement 2 -
so nothing can be said abt the value of x
now combining both the statements .....
we know that both x,y are non n...
Aha...! Never thought of this perspective :). I always assumed ab was the product of a and b and not as two digits of the number. I guess it cannot be assumed unless specified :)
ab = 10a + b
10a is even.
b+1 is div by 4 --> b is odd.
so even + odd = odd
So only ii is enough to answer
2 2
Hi bhars,
i think the ans is III...i.e the Q can be answered by using both the statements together.
(a) implies tat '#' cud b '+' or '-'
(b) implies tat '#' cud b '+' or '*'
so no definite ans considering the statements individually,BUT if we combine them
then '#' sign ...
If the symbol # represents one of the following operations: addition, subtraction , multiplication or division, what is the value of 10#20?
a.2#0 =2
b.2#2 = 4.
:) Bharathi
Thanks for this tip.
All u can say is b is odd. a could be odd (in which case ab would be odd) or a could be even(in which case ab would be even). Answer as said by Arcade, is 4.
When dealing with powers, you should see a few things.
(i) The sign of those numbers
(ii) whether the powers are odd or even
i think the answer 2 the first question shud b choice 3.. from second option we get b is an odd number.. but we don't know anthg abt a.. it can even b a frction.. from the fact that a is a multiple of 3, we know that a is also an integer. so we can safely say that ab will b odd...
How come both the statements can hold true at the same time !!
I wud say
take a=3k
b is odd as (b+1) divisible by 4
so No.=ab= 3bk=Odd no. x k
Now depending on k the No. wud change so it shud b IV
What do u say about a=12
hi shub
I think the correct answer is not II. it shud be III
a is divisible by 3, so it is an odd number.
(b+1) is divisible by 4,so (b+1) is a even number and hence b an odd number
As both a and b are odd numbers their product can never be an even number. therefore ab is an odd numbe...