NUMBER THEORY

If both 112 and 33 are factors of the number a * 43 * 62 * 1311, what is the smallest possible value of 'a'?
121
3267
363
33
37

Correct answer
Explanatory answer
Divisors; Prime factors
Hard



Find the largest five digit number that is divisible by 7, 10, 15, 21 and 28.
99,840
99,900
99,960
99,990
99,970

Correct answer
Explanatory answer
Test of divisibility
Medium



Anita had to multiply two positive integers. Instead of taking 35 as one of the multipliers, she incorrectly took 53. As a result, the product went up by 540. What is the new product?
1050
540
1440
1520
1590


Correct answer
Explanatory answer
Word Problem
Easy



Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?
(x - z)2 y is even
(x - z) y2 is odd
(x - z) y is odd
(x - y)2 z is even
(x + y)3 z is even


Correct answer
Explanatory answer
Operations on Odd & Even integers
Medium



When a number is divided by 36, it leaves a remainder of 19. What will be the remainder when the number is divided by 12?
10
7
19
192
None of these


Correct answer
Explanatory answer
Remainders
Medium



The sum of the first 100 natural numbers, 1 to 100 is divisible by ____
2, 4 and 8
2 and 4
2
100
None of these

Correct answer
Explanatory answer
Sum of AP and divisibility
Medium



How many different factors does 48 have, excluding 1 and 48?
12
4
8
10
None of these


Correct answer
Explanatory answer
Number of factors
Medium



1025 - 7 is divisible by _____
2
3
9
Both (2) and (3)


Correct answer
Explanatory answer
Test of divisibility
Easy



Find the G.C.D of 12x2y3z2, 18x3y2z4, and 24xy4z3
6xy2z2
6x3y4z3
24xy2z2
24xy3z2
18x2y2z3


Correct answer
Explanatory answer
HCF or GCD
Medium



What is the value of M and N respectively? If M39048458N is divisible by 8 & 11; where M & N take integer values from 0 to 9, inclusive?
M = 7; N = 8
M = 8; N = 6
M = 6; N = 4
M = 5; N = 4
M = 4; N = 6


Correct answer
Explanatory answer
Test of divisibility
Medium



48 students have to be seated such that each row has the same number of students as the others. If at least 3 students are to be seated per row and at least 2 rows have to be there, how many arrangements are possible?
4
10
8
7
6


Correct answer
Explanatory answer
Counting Methods
Medium



If two fractions, each of which has a value between 0 and 1, are multiplied together, the product will be ___
always greater than either of the original fractions
always less than either of the original fractions
sometimes greater and sometimes less than either of the original fractions
remains the same
never less than either of the original fractions




Correct answer
Explanatory answer
Properties of fractions
Easy
TANCET 2008



Three Vice Presidents (VP) regularly visit the plant on different days. Due to labour unrest, VP (HR) regularly visits the plant after a gap of 2 days. VP (Operations) regularly visits the plant after a gap of 3 days. VP (sales) regularly visits the plant after a gap of 5 days. The VPs do not deviate from their individual schedules. CEO of the company meets the VPs when all the three VPs come to the plant together. CEO is on leave from January 5th to January 28th, 2012. Last time the CEO met the VPs on January 3, 2012. When is the next time the CEO will meet all the VPs?
February 6, 2012
February 7, 2012
February 8, 2012
February 9, 2012
None of the above




Correct answer
Explanatory answer
LCM & Common Multiples
Moderate
XAT 2012



How many divisors does 7200 have?
20
4
54
32


Correct answer
Explanatory answer
Number of factors
Moderate



What is the highest power of 7 that will divide 5000! without leaving a remainder? (5000! means factorial 5000)
4998
714
832
816


Correct answer
Explanatory answer
Factorial
Moderate



'a' and 'b' are the lengths of the base and height of a right angled triangle whose hypotenuse is 'h'. If the values of 'a' and 'b' are positive integers, which of the following cannot be a value of the square of the hypotenuse?
13
23
37
41


Correct answer
Explanatory answer
Properties of perfect squares
Easy



If x, y, z are chosen from the three numbers, -3, and 2, what is the largest possible value of the expression z2?

16
24
36
54

Correct answer
Explanatory answer
Number Properties
Easy
TANCET 2008



If ( 0.004 * 10a )( 0.32 * 10b ) = 128 * 103, a + b = ?

3
5
6
8
-2