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Math Revolution Approach (PS) 17 Sep 2017, 18:46
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[GMAT math practice question]

If 3 persons are selected at random from 8 persons for 3 positions present, vice-present, and secretary, how many such ways are possible?

A. 56
B. 70
C. 240
D. 336
E. 1680

=>

8P3 = 8 x 7 x 6 = 336

Ans: D
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Math Revolution Approach (PS) 20 Sep 2017, 00:57
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[GMAT math practice question]

What is the range of 25 consecutive even numbers?

A. 44
B. 46
C. 48
D. 50
E. 52

=>

50 – 2 = 48

Ans: C
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[GMAT math practice question]

For a positive integer n, if 5^n is a factor of 25!, but 5^{n+1} is not a factor of 25!, what is the value of n?

A. 5
B. 6
C. 7
D. 8
E. 9

=>

25! = 1 x 2 x … x 5 x … x 10 x … x 15 x … x 20 x … x 25
= 1 x … x 4 x 6 x … x 9 x 11 x … x 14 x 16 x … x 19 x 21 x … x 24 x 5 x 10 x 15 x 20 x 25
= 1 x … x 4 x 6 x … x 9 x 11 x … x 14 x 16 x … x 19 x 21 x … x 24 x ( 5 x 5 x 2 x 5 x 3 x 5 x 4 x 5^2 )
= 1 x … x 4 x 6 x … x 9 x 11 x … x 14 x 16 x … x 19 x 21 x … x 24 x (2 x 3 x 4 x 5^6 )

Thus n = 6.

Ans: B
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Math Revolution Approach (PS) 24 Sep 2017, 19:24
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[GMAT math practice question]

What is the number of multiples of 4 between 25 and 26, inclusive?

A. 8
B. 9
C. 10
D. 11
E. 12

=>

( 2^6 - 2^5 ) / 4 + 1 = 32/4 + 1 = 8 + 1 = 9

Ans: A
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[GMAT math practice question]

There are 5 integers and x≤y≤r≤s≤t. If the median of them is 80 and the average (arithmetic mean) of them is 100, what is the smallest possible value of t?

A. 110
B. 120
C. 130
D. 140
E. 150

=>

In order to have the smallest value of t, we need to maximize x, y and r. Then we have x = 80, y = 80 and r = 80. After that, in order to have the smallest value of t, we need to maximize s and so we have s = 130 and t = 130.

Ans: C
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Math Revolution Approach (PS) 27 Sep 2017, 01:40
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[GMAT math practice question]

The formula for the sum of squares of integer between 1 and n is n(n+1)(2n+1) / 6 = 1^2 + 2^2 + … + n^2. The is the value of 11^2 + 12^2 + … + 20^2?

A. 2470
B. 2475
C. 2480
D. 2485
E. 2490

=>

11^2 + 12^2 + … + 20^2
= ( 1^2 + 2^2 + … + 20^2 ) – (1^2 + 2^2 + … + 10^2)
= 20∙21∙41/6 - 10∙11∙21/6
= 2870 – 385
= 2485

Ans: D
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Math Revolution Approach (PS) 28 Sep 2017, 02:31
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[GMAT math practice question]

If x+(1/x)=4, what is the value of x^2+(1/x)^2?

A. 12
B. 13
C. 14
D. 15
E. 16

=>

x^2+(1/x)^2 = ( x + 1/x )^2 – 2x(1/x) = 4^2 – 2 = 16 - 2 = 14

Ans: C
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Math Revolution Approach (PS) 29 Sep 2017, 01:29
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[GMAT math practice question]

What is the area of the triangle with points (2,4), (3,6), (5,2)?

A. 4
B. 5
C. 6
D. 7
E. 8

=>

The area of the triangle with points (a,b), (c,d) and (e,f) is

1/2|a c b d e a f b |= 1/2| ad-bc+cf-de+eb-af |
1/2|2 3 4 6 5 2 2 4 |= 1/2| 12-12+6-30+20-4 |= 1/2∙8=4

Ans: A
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[GMAT math practice question]


What is the product of all the roots on the equation (x-2)2=|x-2|?

A. 2
B. -2
C. 3
D. -3
E. 6

=>

(x-2)^2=|x-2|
⬄ |x-2|^2=|x-2|
⬄ |x-2|^2-|x-2| = 0
⬄ |x-2| ( |x-2| - 1 ) = 0
⬄ |x-2| = 0 or |x-2| = 1
⬄ x = 2 or x-2 = ±1
⬄ x = 2 or x = 2 ±1
⬄ x = 2 or x = 3 or x = 1
1 * 2 * 3 = 6

Ans: E
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Math Revolution Approach (PS) 01 Oct 2017, 18:21
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[GMAT math practice question]

If 3^x>10, which of the following must be true?

I. x>2
II. x>3
III. x>4

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

=>
3^x>10 > 9 = 3^2
Then, we have x > 2.abc…
Thus x > 2.

Therefore, A is the answer.
Answer: A
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[GMAT math practice question]

If n is the product of 3 different prime numbers, how many factors does n have except 1 and n?

A. 6
B. 7
C. 8
D. 9
E. 10

=>

n = p*q*r where p, q and r are different prime numbers.
Then the number of factors of n is (1+1)(1+1)(1+1) = 8 including 1 and n, since the exponents of p, q and r are 1.
Thus the number of factors of n except 1 and n is 8 – 2 = 6.

Answer: A
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[GMAT math practice question]

n number of people are attending a meeting. All of them shake hands with each other. If all attendees shake hands 210 times, what is the value of n?

A. 15
B. 19
C. 20
D. 21
E. 25

=>

nC2 = n(n-1)/2 = 210
n(n-1) = 420
n(n-1) – 420 = 0
n^2 – n – 420 = 0
(n-21)(n+20) = 0
n = 21 or n = -21
n = 21 since n must be positive.

Answer: D
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[GMAT math practice question]

Which of the following inequalities is equal to |2x-|x||<6?

A. -2<x<0
B. 0<x<6
C. -2<x<6
D. -2<x<2
E. -6<x<6

=>

We should split real number of x into two cases x ≥ 0 and x < 0.

Case 1: x ≥ 0
|2x-|x||<6 ⬄ | 2x – x | < 6 ⬄ |x| < 6 ⬄ -6<x<6.
From the assumption of the case, x ≥ 0, we have 0 ≤ x < 6.

Case 2: x < 0
|2x-|x||<6 ⬄ | 2x + x | < 6 ⬄ |3x| < 6 ⬄ |x| < 2 ⬄ -2<x<2.
From the assumption of the case, x < 0, we have -2<x<0.

Thus, we have -2 < x < 6.

Answer: C
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[GMAT math practice question]

When | 1 - √2 |+| 1 - √3 |+| √2 + √3 | = ?

A. -2
B. -1
C. 0
D. 1
E. 2

=>
| 1 - √2 |+| 1 - √3 |+| √2 + √3 |
= -( 1 - √2 ) – ( 1 - √3 ) + ( √2 + √3 )
= -1 + √2 – 1 + √3 + √2 + √3
= -2

Answer: A
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[GMAT math practice question]

If 8x=2y, what is the value of x, in terms of y?

A. x=2^{3y-2}
B. x=4y
C. x=4^{y-2}
D. x=2^{y-3}
E. x=2y

=>

8x = 2^y ⬄ 2^3x = 2^y ⬄ x = 2^{y-3}

Answer : D
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[GMAT math practice question]

Which of the following is closest to (1+2^18)/(2^4+2^10)?

A. 2^5
B. 2^6
C. 2^7
D. 2^8
E. 2^9

=>

(1+2^18)/(2^4+2^10) = (1+2^18)/(2^4(1+2^6)) = (1+2^6)(1-2^6+2^12)/(2^4(1+2^6))
= (1-2^6+2^12)/2^4 ≒ 2^8

Therefore, the answer is D.

Answer: D
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[GMAT math practice question]

If 0.010<x-√5<0.011, approximation of 1/√5-1/x is which of the following options?

A. 0.01
B. 0.002
C. 0.02
D. 0.003
E. 0.03

=>

1/√5-1/x = x-√5/x√5

From 0.010<x-√5<0.011, we have 0.010 + √5<x <0.011 + √5.
We have 1/0.010+ √5 < 1/x < 1/0.011+ √5 or 1/0.010√5+5 < 1/x√5 < 1/0.011√5+5.
0.010/0.010√5+5 < x-√5/x√5 < 0.011/0.011√5+5.
The approximation of x-√5/x√5 is 0.01/5=0.002

Thus, the answer is B.


Answer: B
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If x-5=√x+√5 , which of followings is true?

A. x^2+12x+16 = 0
B. x^2-12x+16 = 0
C. x^2+6x+8 = 0
D. x^2-6x+8 = 0
E. x^2+6x-8 = 0

=>
x-5=√x+√5 is equivalent to (√x+√5)(√x-√5)=√x+√5 or √x+√5=1
√x=√5 + 1
x = 5 + 2√5 + 1 = 6 + 2√5
(x-6)^2 = 20
x^2 – 12x + 36 = 20
x^2 – 12x + 16 = 0

Therefore, the answer is B.

Answer: B
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[GMAT math practice question]

(6^3)a+(6^2)b+6c+d=821, where a, b, c, and d are integers from 0 to 5, inclusively, c=?

A. 0
B. 1
C. 2
D. 3
E. 4

=>
821 = 6*136 + 5
136 = 6*22 + 4
22 = 6*3 +4
821 = 6*136 + 5 = 6*(6*22+4) + 5 = 6 * ( 6 * (6 *3 + 4) + 4 ) + 5
= 6 * ( 6^2*3 + 6*4 + 4 ) + 5
= 6^3*3 + 6^2*4 + 6*4 + 5
= 6^3*a + 6^2*b + 6*c + d
Thus a = 3, b = 4, c = 4 and d = 5.
Therefore, the answer is E.

Answer: E
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[GMAT math practice question]

Attachment:
1023.png
1023.png [ 2.42 KiB | Viewed 1465 times ]

In the above table, scores and numbers of people are shown. If the median score is not represented as the score shown on the table, which of the following scores can be the value of x?

A. 2
B. 3
C. 4
D. 5
E. 6

=>
The sum of numbers for a+1 and a+2 is 15 = 7 + 8. If 2 + 8 + x = 15, we don’t have the median on the table.
Thus, 10 + x = 15 and we have x = 5.

Therefore, the answer is D.
Answer : D
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