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GMAT - Problem Solving - Arithmetic

The value of is how many times the value of 2^-17 (more)

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 (23 + 22 + 2 + 1) / 5

2-17 (15)/5

2-17 * 3

Answer is 3

Option C is correct

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

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

{ I.\quad \left( \sqrt { 82 }  \sqrt { 82 } \right) }^{ 2 }\\ \\ II.\quad 82\sqrt { 82 } \\ \\ III.\quad \frac { \sqrt { 82 } \sqrt { 82 } }{ 82 }

(A) None
(B) I only
(C) III only
(D) I and II
(E) I and III

Statement I

{ \left( \sqrt { 82 } +\sqrt { 82 } \right) }^{ 2 }\\ =\quad { \left( 2\sqrt { 82 } \right) }^{ 2 }\\ =\quad 4*82\quad =\quad 328

Yes

Statement II

\\ \\ 82\sqrt { 82 }

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

Statement III

\\ \\ \frac { \sqrt { 82 } \sqrt { 82 } }{ 82 } \\ \\ =\frac { 82 }{ 82 } =1

Can be written as an integer

Correct option E.

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? (more)

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.

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? (more)

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