How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 53

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IMPORTANT

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What is the remainder when $128^{1000}$ is divided by $153$ ?

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Important Questions on Number Systems

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IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 54

Find the remainder when

50^{51^{52}}

is divided by

11

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 55

Find the remainder when

32^{33^{34}}

is divided by

11

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 56

Find the remainder when

30^{72^{87}}

is divided by

11

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 57

Find the remainder when

50^{56^{52}}

is divided by

11

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 58

Find the remainder when

33^{34^{35}}

is divided by

7

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 59

Let

S_{m}

denote the sum of the squares of the first

m

natural numbers. For how many values of

m < 100

, is

S_{m}

a multiple of

4

?

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 60

Let

S_{m}

denote the sum of the cubes of the first

m

natural numbers, for how many values will the sum of cubes of the first

m

natural numbers be a multiple of

5 (if m < 50)

?

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IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 61

How many integer values of

x and y satisfy the expression 4 x + 7 y = 3

where

| x | < 1000 and | y | < 1000

?