Number System - Problem Set 1

Saturday, April 29, 2006

Test your knowledge

Problems are based on the basics which we have covered in number system. Try to solve the questions first and then look at the answers. If you have any doubts refer to Basics 1 and Basics 2 of Number System.

Questions:

Q1) 8 odd natural numbers add up to a total of 77. Which one is true?
a) One of the number has to be 1.
b) One of the number has to be 3.
c) One of the number has to be 7.
d) One of the number has to be 5.
e) There is no solution for this.

Q2) P is product of three consecutive natural numbers, Which one is true?
a) P will always be divisible by 24.
b) P will always be divisible by 10.
c) P will always be divisible by 6.
d) No solution.

Q3) 45556 x 23843 = ?
a) 1086194751
b) 1087161425
c) 1086194723
d) 1086191708

Q4) 123 + 345 + 524 + 245 = ?
a) 1137
b) 1224
c) 1076
d) 1138

Q5) 47^4 = ?
a) 4873634
b) 4879681
c) 4878646
d) 4870682

Q6) Which of the numbers are prime?
a) 67
b) 113
c) 317
d) 144

Solutions:

A1): e, Do you remember, sum of any odd numbers of even number (i.e 8) is even. We have seen this in basics.

A2): c, We have seen that product of 3 consecutive numbers is always divisible by 6, If it would have been mentioned that the first number of the three numbers is even, then the product would be always divisible by 24..

A3): d, Why? The units digits of the numbers are even and odd, so even x odd = even, only one option satisfies this, hence by elimination. Or, You could just multiply the last digits of the two numbers and looked for the last digit of the options.

A4): a, Three numbers are even and one is odd so, odd + even + even + even = odd. Only one option is odd, hence by elimination. Or, just add up all the last digits of the numbers and look for the last digit in the options. Quick maths will help you here.

A5): b, Anything raised to an odd number (here base is odd), the result is odd, hence by elimination. There is a concept of cyclicity, which I will cover later.

A6): a, b and c are primes. Try it with the square root method that we have seen earlier, I will explain for 67,
Step 1) The square root of 67 will lie in between of 8 and 9, we take the greater number i.e 9,
Step 2) Try to divide 67 with all the primes less than 9, i.e 2, 3, 5, 7. None of the numbers divide 67, hence 67 is a prime number.

*There will be more Problem Sets on Number System in which I will cover past CAT questions and other CAT/GMAT like questions.