7
Q:

# 243 has been divided into three parts such that half of the first part, one - third of the second part and one - fourth of the third part are equal. The largest part is ?

Q:

Find the least number with which 16200 should be multiplied, to make it a perfect cube ?

 A) 45 B) 48 C) 360 D) 36

Explanation:

16200 = $\inline \fn_jvn \small 2^{3}x3^{4}x5^{2}$

A perfect cube has a property of having the indices of all its prime factors divisible by 3.

Required number = $\inline \fn_jvn \small 3^{2}x5$ = 9x5 = 45.

1 13
Q:

Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is :

 A) 83 B) 89 C) 85 D) 79

Explanation:

Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F of 551 and 1073 = 29;
First number = 551/29 = 19
Third number = 1073/29 = 37.
Required sum = 19 + 29 + 37 = 85.

1 10
Q:

The sum of the two digits of a number is 8. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number ?

 A) 28 B) 19 C) 37 D) 17

Explanation:

Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 8 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 1 and Q = 7
The required number is = 17

1 7
Q:

The series of differences between consecutive prime numbers is represented as Cp1, Cp2, Cp3, .... Cpn , Whare Cp1 is the difference between the second and the first prime number. Find the sum of series when n = 23, given that the 23rd prime number is 83 ?

 A) 87 B) 81 C) 83 D) 85

Explanation:

Cp1 = p2 - p1 ,
Cp2 = p3 - p2
..
..
..
Cp23 = p24 - p23
Sum of series = (p2-p1) + (p3-p2) + .....(p23-p22) + (p24-p23)
All terms get cancelled, except p1 = 2 and p24 = 89
So Sum = -p1 + p24
Sum of series = -2 + 89 = 87

4 11
Q:

Total 100 members are writing exam. In that 48 members are writing first exam, 45 members are writing second exam and 38 members are writing third exam. 5 members are writing all the three exams. How many members are writing 2 exams ?

 A) 26 B) 23 C) 27 D) 21