How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 74

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What is the highest power of $3$ available in the expression $(58! - 38!)$ ?

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Important Questions on Number Systems

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 75

Find the remainder when the number represented by

22334

raised to the power

(1^{2} + 2^{2} + 3^{2} + . . . . + 66^{2})

is divided by

5

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 76

What is the total number of divisors of the number

12^{33} \times 34^{23} \times 2^{70}

?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 77

Which of the following will represent the sum of factors of the number

12^{33} \times 34^{23} \times 2^{70}

( such that only odd factors are counted)?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 78

What is the remainder when

{(1!)}^{3} + {(2!)}^{3} + {(3!)}^{3} + {(4!)}^{3} + . . . + {(1152!)}^{3}

is divided by

1152 ?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 79

A set $S$ is formed by including some of the first one thousand natural numbers. $S$ contains maximum number of numbers such that they satisfy the following conditions:

$1 .$ No number of the set $S$ is prime.

$2 .$ When the number of the set $S$ are selected two at a time, we always see co-prime numbers.

What is the number of elements in the set $S$ ?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 80

Find the last two digits of the following number

$101 \times 102 \times 103 \times 197 \times 198 \times 199$

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 81

Find the last two digits of the following number

65 \times 29 \times 37 \times 63 \times 71 \times 87

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 82

Find the last two digits of the following number

$65 \times 29 \times 37 \times 63 \times 71 \times 87 \times 85$