Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 5

EASY

CAT

IMPORTANT

Earn 100

Let $a_{1}, a_{2}, \dots$ be integers such that $a_{1} - a_{2} + a_{3} - a_{4} + \dots + (- 1)^{n - 1} a_{n} = n$ , for all $n \geq 1$ . Then $a_{51} + a_{52} + \dots + a_{1023}$ equals

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Important Questions on X+2 Maths

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 6

Let

a_{1}, a_{2}, \dots, a_{52}

be positive integers such that

a_{1} <

a_{2} < \dots < a_{52}

. Suppose their arithmetic mean is one less than the arithmetic mean of

a_{2}, a_{3}, \dots, a_{52}

. If

a_{52} = 100

, then the largest possible value of

a_{1}

is

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 7

Let

x, y, z

be three positive real numbers in a geometric progression such that

x < y < z

. If

5 x, 16 y

, and

12 z

are in an arithmetic progression, then the common ratio of the geometric progression is

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 8

The value of the sum

7 \times 11 + 11 \times 15 + 15 \times 19 + \dots + 95 \times 99

is

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 9

If the square of the

7 th

term of an arithmetic progression with positive common difference equals the product of the

3 rd and 17 th

terms, then the ratio of the first term to the common difference is

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 10

If the product of the three consecutive positive integers is

15600

then the sum of the squares of these integers is

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 11

Let

a_{1}, a_{2}, . . ., a_{3 n}

be an arithmetic progression with

a_{1} = 3 and a_{2} = 7

. If

a_{1} + a_{2} + . . . + a_{3 n} = 1830

, then what is the smallest positive integer

' m'

such that

m \times (a_{1} + a_{2} + . . . + a_{n}) > 1830

?

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 12

Let

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}

be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with

2 a_{3}

. If the sum of the numbers in the new sequence is

450

, then

a_{5}

is

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 3 - X+2 Maths>Practice Exercises>Q 13

An infinite geometric progression

a_{1}, a_{2}, a_{3} . . .

has the property that

a_{n} = 3 (a_{n + 1} + a_{n + 2} + . . .)

for every

n \geq 1

. If the sum

a_{1} + a_{2} + a_{3} + . . . = 32

, then

a_{5}

is