LEAP Administrator
2 years ago
**Problem Solving** |
**Arithmetic**

The value of (2^{-14} 2^{-15} 2^{-16} 2^{-17}) / 5 is how many times the value of 2^{-17}

A. 3/2

B. 5/2

C. 3

D. 4

E. 5

(2^{-14} + 2^{-15} + 2^{-16}^{ }+ 2^{-17}) / 5

2^{-17} (2^{3} + 2^{2} + 2 + 1) / 5

2^{-17} (15)/5

2^{-17} * 3

Answer is 3

Option C is correct

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LEAP Administrator
2 years ago
**Problem Solving** |
**Arithmetic**

Which of the following expressions can be written as an integer?

(A) None

(B) I only

(C) III only

(D) I and II

(E) I and III

Statement I

Yes

Statement II

No further simplification possible. Can't be written as an integer

Statement III

Can be written as an integer

Correct option E.

LEAP Administrator
2 years ago
**Problem Solving** |
**Arithmetic**

For any positive integer n, the sum of the first n positive integers equals n(n 1)/2. What is the sum of all the even integers between 99 and 301?

A. 10,100

B. 20,200

C. 22,650

D. 40,200

E. 45,150

We have to find out the sum : 100 + 102 + 104 + . . . + 300

= 2 (50 + 51 + 52 + . . . + 150)

{We can use sum of an Arithmetic progression formula, but for the sake of the question we can use the formula in the question}

= 2 (1 + 2 + 3 + . . . + 50 + 51+ . . . + 150 - (1 + 2 + 3 + . . . + 49))

= 2 (150*151/2 - 49*50/2)

= 150*151 - 49*50

= 20200

B is correct.

LEAP Administrator
2 years ago
**Problem Solving** |
**Arithmetic**

When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

Given that

when x is divided by y, the remainder is 9

also given x/y = 96.12 ... Eq 2

we can say that

x = 96y + 9

from Eq. 2

(96y + 9) / y = 96.12

96 + 9/y = 96.12

9/y = 0.12

y = 9/0.12 = 75