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# Math Revolution Approach (PS)

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Math Revolution GMAT Instructor
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25 Oct 2017, 01:20
[GMAT math practice question]

The number of club X’s members is increased by 20 percent every year. If the number of members of the club X in 2000 was m, how many number of members in 2005 are greater than that of members in 2004?

A. (0.2)(1.2)^4m
B. (0.8)(1.2)^4m
C. (0.2)(1.2)^5m
D. (0.8)(1.2)^5m
E. (0.8)^4(1.2)^4m

=>

(1.2)^5m – (1.2)^4m = (1.2)^4m(1.2-1) = (0.2)(1.2)^4m

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25 Oct 2017, 23:47
[GMAT math practice question]

There are 3 machines with the same work rate. If it took t hours for 3 machines to work and took t+2 hours for 2 machines when working together, what is the value of k?

A. 4
B. 5
C. 6
D. 7
E. 9

=>

Assume X is the time one machine takes to work.

1/T=3/X and 1/T+2=2/X

X = 3T and X = 2(T+2).
We have 3T = 2T + 4 or T = 4.

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27 Oct 2017, 00:31
[GMAT math practice question]

Let function f(x)=(x-a)(x-b). If f(10)=f(20)=0, f(30)=?

A. 50
B. 100
C. 150
D. 200
E. 250

=>

Since f(10) = f(20) = 0, f(x) = (x-10)(x-20).
f(30) = (30-10)(30-20) = 20*10 = 200.

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29 Oct 2017, 17:05
[GMAT math practice question]

(1/26)+(1/27)+……+(1/49)+(1/50) is included in which of the following ranges?

A. (1/6)~(1/5)
B. (1/5)~91/4)
C. (1/4)~(1/3)
D. (1/3)~(1/2)
E. (1/2)~1

=>

1/26 > 1/50, 1/27 > 1/50, …, 1/49 > 1/50
(1/26)+(1/27)+……+(1/49)+(1/50) > 1/50 + 1/50 + … + 1/50 = (1/50)*25 = 1/2.
1/26 < 1/25, 1/27 < 1/25, … , 1/49 < 1/25, 1/50 < 1/25.
(1/26)+(1/27)+……+(1/49)+(1/50) < 1/25 + 1/25 + … + 1/25 = (1/25)*25 = 1.

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29 Oct 2017, 17:07
[GMAT math practice question]

Tom traveled the entire 90 km trip. If he travelled the first 18 km of the trip at a constant rate of 36 km per hour and the remaining trip at a constant rate of 72 km per hour, what is his average speed?

A. 30 km/h
B. 36 km/h
C. 45 km/h
D. 48 km/h
E. 60 km/h

=>

90 / (18/36 + 72/72) = 90 / 1.5 = 60

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Re: Math Revolution Approach (PS)  [#permalink]

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01 Nov 2017, 00:58
[GMAT math practice question]

If f(x+y) = f(x)f(y), which of followings can be the value of f(0)?

I. 0
II. 1
III. 2

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

=>

When we plug in x = 0 and y = 0, we have f(0) = f(0)f(0) or f(0)f(0) – f(0) = 0.
Then f(0){ f(0) – 1 } = 0, so we have f(0) = 0 or f(0) = 1.

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Joined: 01 Jan 2016
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Re: Math Revolution Approach (PS)  [#permalink]

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01 Nov 2017, 02:09
MathRevolution wrote:
A larger cube has 27 cubic inch as a volume and in the cube there are 27 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 27 smaller cubes and the surface area of the larger cube, in square inch?
A. 54
B. 64
C. 81
D. 108
E. 120

ANS: If we calculate 6*27-6*9=108, D becomes our answer.

Can you explain this one ?
Math Revolution GMAT Instructor
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02 Nov 2017, 00:11
[GMAT math practice question]

If x=-1 and n is the sum of all prime numbers less than 100, what is the value of x^n+x^{n+1}+x^{n+2}+x^{n+3}+x^{n+4}+x^{n+5}?

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

=>

Whatever the value of n is, (-1)^n+(-1)^{n+1}+(-1)^{n+2}+(-1)^{n+3}+(-1)^{n+4}+(-1)^{n+5} = 0, since two consecutive integer n and n+1 always have an odd integer and an even integer, and so (-1)^n+(-1)^{n+1} = 0.

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Re: Math Revolution Approach (PS)  [#permalink]

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02 Nov 2017, 09:22
bhateja wrote:
MathRevolution wrote:
A larger cube has 27 cubic inch as a volume and in the cube there are 27 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 27 smaller cubes and the surface area of the larger cube, in square inch?
A. 54
B. 64
C. 81
D. 108
E. 120

ANS: If we calculate 6*27-6*9=108, D becomes our answer.

Can you explain this one ?

The edge of the larger cube is 3 and the area of one face is 9.
And the cube has 6 faces.

The edge of the smaller cube is 1 and each face has the area 1.

6*27 means the sum of 6 faces area of the smaller cube times 27 cubes.
6*9 is the number of faces 6 times the area of each face 9.

6*27 - 6*9 is the answer.

Happy Studying !!!
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04 Nov 2017, 17:20
[GMAT math practice question]

When x/y = 1.2, (x^2-y^2)/(x^2+y^2) =?

A. 10/51
B. 11/51
C. 10/61
D. 11/61
E. 11/71

=>

x/y = 6/5.
(x^2-y^2)/(x^2+y^2) = ((x/y)^2-1)/((x/y)^2+1) = ((6/5)^2 – 1 ) / ((6/5)^2 + 1 )
= (6^2-5^2)/(6^2+5^2) = (36-25)/(36+25) = 11/61

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05 Nov 2017, 17:25
[GMAT math practice question]

(3^3+3^4+3^5+3^6)^2=?

A. 2^43^65^2
B. 2^63^45^2
C. 2^83^65^2
D. 2^63^85^2
E. 2^63^65^2

=>
(3^3+3^4+3^5+3^6)^2= (3^3(3^0+3^1+3^2+3^3))^2=3^6(1+3+9+27)^2=3^640^2=3^62^65^2

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05 Nov 2017, 17:27
[GMAT math practice question]

Which of the following equations has a unique integer solution?

A. y=3x
B. y=(x/3)+4
C. y=√2x
D. y=(1/2)x
E. y=(-1/x)+2

=>

A. x = 0, y = 0 / x = 1, y = 3
B. x = 0, y = 4 / x = 3, y = 5
C. y=√2x has a unique integer solution, that is, x = 0 and y = 0. If x is not 0, y is an irrational number, which is not an integer.
D. x = 0, y = 0 / x = 2, y = 1
E. x = 1, y = 1 / x = -1, y = 3

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08 Nov 2017, 23:57
[GMAT math practice question]

What of the followings is the range of X = 1 + (1/2^2) + (1/3^2) + ...... + (1/100^2),

A. 0 < X < 1
B. 1 < X < 2
C. 2 < X < 3
D. 3 < X < 4
E. 4 < X < 5

=>

1/A^2 < 1/{(A-1}A} = 1/(A-1) – 1/A

It is clear that 1 + (1/2^2) + (1/3^2) + ...... + (1/100^2) > 1.

1 + (1/2^2) + (1/3^2) + ...... + (1/100^2)
< 1 + 1/(1∙2) + 1/(2∙3) +1/(3∙4) + … + 1/(99∙100)
= 1 + ( 1/1 – 1/2 ) + ( 1/2 – 1/3 ) + … + (1/99 – 1/100)
= 1 + 1/1 – 1/100 = 2 – 1/100 < 2

Thus 1 < X < 2.

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09 Nov 2017, 00:00
[GMAT math practice question]

The probability that an event A occurs is 1/2 and the probability that an even B occurs is 1/3. If event A and event B are independent, what is the probability that event A occurs but event B does not occur?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6

=>

Since events A and B are independent, P(A∩B) = P(A) ∙P(B).
The probability P(A-B) = P(A) - P(A∩B) = P(A) - P(A) ∙P(B) = 1/2 – (1/2)(1/3) = 1/2 – 1/6 = 2/6 = 1/3.

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12 Nov 2017, 18:03
[GMAT math practice question]

What is the sum of the remainders when the first 50 positive integers are divided by 5?

A. 60
B. 70
C. 80
D. 90
E. 100

=>

1, 2, 3, 4, 5 have remainders 1, 2, 3, 4, 0 and the sum of their remainders is 1 + 2 + 3 + 4 + 0 = 10.
6, 7, 8, 9, 10 have remainders 1, 2, 3, 4, 0 and the sum of their remainders is 1 + 2 + 3 + 4 + 0 = 10.

46, 47, 48, 49, 50 have remainders 1, 2, 3, 4, 0 and the sum of their remainders is 1 + 2 + 3 + 4 + 0 = 10.

10 * 10 = 100

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12 Nov 2017, 18:04
[GMAT math practice question]

In a pin factory, it needs to produce 100,000 pins every day, and 5 machines take x hours to produce 100,000 pins. One day, one of the machines is out of order, so only 4 machines worked. These four machines took x+2 hours to produce 100,000 pins, and each machine’s work rates are the same. What is the value of x?

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

=>

Assume T is the time that one machine takes to produce 100,000 pins.

1/x = 5/T and 1/(x+2) = 4/T
5x = T and T = 4(x+2)
5x = 4(x+2)
5x = 4x + 8
x = 8.

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15 Nov 2017, 00:52
[GMAT math practice question]

In the normal x-y coordinate plane there are 4 points A(-1,3), B(3,3), C(-1,7), and D(3,7). If a line passing through the origin bisects the area of the rectangle ABCD, what is the slope of the line?

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

=>

The line should pass through the center of the rectangle ABCD.
Then the center is ((-1+3)/2, (3+7)/2) or (1,5)
The slope of the line passing though (0,0) and (1,5) is 5-0/1-0=5.

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16 Nov 2017, 00:42
[GMAT math practice question]

I. 1/2,2/3,3/4,4/5,5/6
II. 1/2,1/3,1/4,1/5,1/6
III. 1/6,2/6,3/6,4/6,5/6

For which of the above lists is the average of the numbers less than the median of numbers?

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

=>
I. The differences between the consecutive terms are 1/6 (= 2/3 – 1/2 ), 1/12 (= 3/4 – 2/3 ), 1/20 (= 4/5 – 3/4 ), and 1/30 (= 5/6 – 4/5). As these are decreasing, the average is smaller than the median.

II. The differences between consecutive terms are - 1/6(= 1/3 – 1/2),-1/12(= 1/4 – 1/3 ), - 1/20(= 1/5 – 1/4), and -1/30(= 1/6 – 1/5). As these are increasing, the average is larger than the median.

III. As the data are symmetric, the average and the median are equal.

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Re: Math Revolution Approach (PS)  [#permalink]

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17 Nov 2017, 00:23
[GMAT math practice question]

Which of the following is true if -3<x<9?

A. |x-3|<4
B. |x-3|<5
C. |x-3|<6
D. |x-3|>4
E. |x-3|>5

=>

|x-a|<b
⟺ -b < x – a < b
⟺ a - b < x < a + b
So, a is the midpoint of the end points a – b and a + b, and
b is half the distance between the end points a – b and a + b.

The midpoint of -3 and 9 is [(-3)+9]/2 = 6/2 = 3. So, a = 3.
Since the distance between -3 and 9 is 12, b = 12/2= 6.
Thus, |x-3| < 6.

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19 Nov 2017, 17:23
[GMAT math practice question]

In how many ways can three boys and four girls line up in a row, if girls take the first and last positions?

A. 28
B. 120
C. 720
D. 1,440
E. 5,040

=>

There are four ways (girls) to fill the first position and three ways (girls left over) to fill the last position. The remaining five positions can be filled by the five remaining children (three boys and two girls) in 5!=120 ways.

By the multiplication rule, there are 4 * 3 * 120 = 1,440 different lines possible.

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# Math Revolution Approach (PS)

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