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IMPORTANT

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$f (x, x) = x^{x}$ and $f (f (x, x)) = x^{x^{x}}$ and so on. What is the value of $f (f (f (f (7, 7))))$ when divided by $5$ ?

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Important Questions on Numbers and Their Properties

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 34

The students of class

10^{th}

of Morgan High School took a test, which had a maximum of

50

marks. The teacher misplaced the text notebooks of two of the students - Robin and Garry; however, she remembered that Garry had scored something between

10

and

15

and Robin something between

32

and

40

. She also remembered that the product of the marks obtained by the two students was also equal to

10

times the marks obtained by two of them. How many marks did Garry scored?

EASY

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 35

The History teacher was referring to a year in the

19^{th}

century. Rohan found an easy way to remember the year. He found that the number, when viewed in a mirror, increased

4.5

times. Which year was the teacher referring to?

EASY

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IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 36

Srini wrote his class

10^{th}

board examination this year. When the result was out, he searched for his hall ticket to see his roll number, but could not trace it. He could remember only the first three digits of the six-digit number as

267

. However, his father remembered that the number was divisible by

11

. His mother gave the information that the number was also divisible by

13

. They tried to recollect the number when all of a sudden Srini told that the number was a multiple of

7

. What were the units digits of the number?

EASY

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IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 37

Prof. Mathur and Prof. Singh attended the All India Historian's meet last week. Prof. Mathur told Prof. Singh, 'I found out that your teaching experience is twice that of mine'. Prof. Singh replied in the affirmative. Prof'. Mathur continued, 'But last time when both of us came for the same meet, I remember that your teaching experience was thrice that of mine'. 'That was

2

years ago.' Prof. Singh said. How many years has Prof. Singh been working?

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IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 40

Raju had to divide

1080

by N, a two-digit number. Instead, he performed the division using M, which is obtained by reversing the digits of N, and ended up with a quotient that was

25

less than what he should have obtained otherwise. If

1080

is exactly divisible both by N and M, find the sum of the digits of N.

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 42

The last digit of the $L C M$ of $(3^{2003} - 1)$ and $(3^{2003} + 1)$ is

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Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 43

a, b, and c are positive integers such that

(a + b + c) = 2003

. Let

E = (- 1)^{a} + (- 1)^{b} + (- 1)^{c}

. Find the number of possible values of E.

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 44

Ajay took a four-digit number in base

5

notation. He subtracted the sum of the digits of the numbers from the number. From the result, he struck off one of the digits. The remaining three digits were

1, 0,

and

2

. Then, the digit struck off by Ajay was:

f(x,x)=xx and f(f(x,x))=xxx and so on. What is the value of f(f(f(f(7,7)))) when divided by 5?

Important Questions on Numbers and Their Properties

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$f (x, x) = x^{x}$ and $f (f (x, x)) = x^{x^{x}}$ and so on. What is the value of $f (f (f (f (7, 7))))$ when divided by $5$ ?