# Free CAT Questions

### Data Sufficiency

• Discussion in CAT
• Created by @shub001
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 n... Read More »
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I know some of my question are dumb but ....er....well, I am dumb too.

Please show me how to solve this DS question.

Given that x and Y are non-negative. What is the value of X?

I 2X+2Y<= 40 II X-2Y >=20

Statement 1 -

2x+2y<=40
that is x+y<=20

(5+15=20 , 8+12=20..... )
so nothing can be said abt the value of x

Statement 2 -

x-2y>=20

(30-2*5=20,40-2*9=22)
so nothing can be said abt the value of x

now combining both the statements .....
we know that both x,y are non negative
and still
x+y = 20 (limiting case ...drop the < sign)
x-2y = 20(limiting case ....drop the > sign)

we now x = 20 and y = 0
no other solution will satisfy ....u can have a try
so the answer is 3 ( i.e we have to use both the statements to get the answer)

HTH
Gautam
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ab = 10a + b

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 :)

Bharathi.
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Hi,

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 Likes
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Hi bhars,
i think the ans is III...i.e the Q can be answered by using both the statements together.
cos...
(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 surely represents '+'...n then we can find the value of 10#20 i.e 10+20=30

regards,
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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
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When dealing with powers, you should see a few things.
(i) The sign of those numbers
(ii) whether the powers are odd or even
(iii) If the numbers are <1 or >1.

Thanks for this tip.
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Is ab an even number ?
I. a is divisible by 3.
II. (b+1) is divisible by 4.

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.

If x^a = y^b > z^c, is x = y > z?
I. a = b > c
II. a = b = c

When dealing with powers, you should see a few things.
(i) The sign of those numbers
(ii) whether the powers are odd or even
(iii) If the numbers are <1 or >1.

Only if all of these are given directly or indirectly, we can solve the problem. Since NOTHING has been said about x, y and z (whether integers, fractions < 1, negative, postive,...) we cannot conclude anything. Answer again is 4.

Bharathi.
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hi
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...
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If x^a = y^b > z^c, is x = y > z?
I. a = b > c
II. a = b = c

III] The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
.

How come both the statements can hold true at the same time !!
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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
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a is divisible by 3, so it is an odd number.
Dan

What do u say about a=12
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hi shub

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??

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 number. i.e the question can be solved using both I and II

If n is a natural number, is n ! < ^x ?
I. n is an even number.
II. x > n

case 1)Taking n as 1 and x as 10, we get 1=1
case 2)with n as 2 and x as 10 , we get 2 < 1.5^10
case 3)with n as 2 and x as 1 , we get 2 > 1.5

so case 2 results r consistent(the other combinations do not result in a consistent 'yes' or 'no')

thus the answer is III..it can be answered using both the statements together.

If x^a = y^b > z^c, is x = y > z?
I. a = b > c
II. a = b = c

sounds tricky!

Dan
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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

If n is a natural number, is n ! < ^x ?
I. n is an even number.
II. x > n

I] The question can be answered by one of the statements alone, but cannot be answered by using the other statement alone.

II] The question can be answered by using either statement alone.

III] The question can be answered by using both the statements together, but cannot be answered by using either statement alone.

IV] The question cannot be answered even by using both statements together.

WE shall follow the same options in all the DS questions.
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