CAT Questions

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Given  65×359×113

⇒2×35×5×79×113 

⇒25×35×59×79×113

Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.

Rainer Weiss, a professor at the Massachusetts Institute of Technology, and Kip Thorne and Barry Barish, both of the California Institute of Technology, were awarded the Nobel Prize in Physics for the discovery of ripples in space-time known as gravitational waves, which were predicted by Albert Einstein a century ago but had never been directly seen.

Let assume the value of a,b &c that will satisfy the equation.
so a=1,b=1,c= -1 or a=1,b= -1 &c=1 or a= -1,b=1,c=1
here all three cases satisfy the equation
assume any one a=1,b=1,c= -1

Hence (a+b)(b+c)(c+a)=(1+1)(1-1)(-1+1) = 0

HURRAYS.

Here given the required digit number is 4 digit.

It must be divisible by 5. Hence, the unit's digit in the required 4 digit number must be 0 or 5. But here only 5 is available.

x x x 5

The remaining places can be filled by remaining digits as 5 x 4 x 3 ways.

Hence, number 4-digit numbers can be formed are 5 x 4 x 3 = 20 x 3 = 60.

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Let the cost price of the bottle = Rs. 100

Selling price of the bottle = Rs. 100 - Rs. 9 = Rs. 91

Then, from the given data,

=> 112 (1/2) - 91 = 15

=> 21 (1/2) = 15

=> 43 = 15

Then 100 = ?

1500/43 = 34.885 =~ 35

Hence, the cost price of the bottle = Rs. 35