How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 120

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CAT

IMPORTANT

Earn 100

$1777$ has exactly $5$ digits when converted to base $' x'$ from the decimal system. What is the minimum possible value of $x$ ?

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Important Questions on Number Systems

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 121

What will be the sum of all natural numbers between

101 and 1000

which on division by

2, 4, 6, 8, 10

leave remainders

1, 3, 5, 7, 9

respectively?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 122

Unit digit of which of the following is the same as the units digits of

a^{17} + b^{17}

For any positive integer value of

a, b

?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 123

How many

4

Digit numbers are there in the decimal system, which have exactly

4

Digits when expressed in Base

6

, Base

7

, Base

8

?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 124

What is the difference between the highest and the least four digit natural numbers that have exactly four digits when expressed in Base

6

and Base

7

.

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How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 125

If

n

is a natural number, then what is the sum of all the possible distinct remainders when

9^{n} + 6^{n} + 4 {^{n} + 11}^{n}

is divided by

10

?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 126

If

x, y, z

and

w

are natural numbers, then what is the sum of all the possible remainders when

9^{x} + 6^{y} + 4^{z} + 11^{z}

is divided by

10

?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 127

What is the maximum possible sum of the number of Mondays and Thursdays in two consecutive years?

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CAT

IMPORTANT

How to prepare for Quantitative Aptitude for the CAT>Chapter 1 - Number Systems>Level of Difficulty>Q 128

In the previous question find the minimum possible sum of the number of Mondays and Thursdays in two consecutive years?