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Math Revolution Approach (PS)

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

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New post 13 Apr 2018, 19:48
MathRevolution wrote:
A ball dropped from a certain height. The height that it reached after rebounding from the floor was 60 percent of the initial height. The height was 292cm when it touched the floor for the third time. What was the initial height?
A. 80cm
B. 90cm
C. 100cm
D. 120cm
E. 130cm

ANS: If we consider the initial height as x, then from x+2(60%)x+2(60%)^2(x)=292, we get x=100. Hence, the correct answer is C.


So initial height is less than the height reached in the third rebound? Strange.


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New post 15 Apr 2018, 18:45
[GMAT math practice question]

Which of the following is equal to x!/(x+1)! + (x+1)!/(x+2)!?

A. 1+1/x
B. 1+1/(x+1)
C. (2x+3)/(x+1)(x+2)
D. 1/{ x(x+1) }
E. (2x-1)/{(x+1)(x+2)}

=>

x! / ( x + 1 )! + ( x + 1 )! / ( x + 2 )!
= x! / {x! * (x+1)} + (x+1)! / { (x+1)! * (x+2) }
= 1/(x+1) + 1/(x+2) = (2x+3)/(x+1)(x+2)

Therefore, C is the answer.
Answer: C
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New post 15 Apr 2018, 18:47
[GMAT math practice question]

Alice is paid at a constant rate of $x per hour for the first 40 hours she works and $30 for each hour she works after the first 40 hours. If Alice works 48 hours and earns $920, what is the value of x?

A. $15
B. $16
C. $17
D. $18
E. $19

=>

Total pay = (rate for first 40 hours)*40 hours + ($30)*(number of additional hours)
x * 40 + ( 48 – 40 ) * 30 = 920
x*40 + 8*30 = 920
x * 40 + 240 = 920
x * 40 = 680
x = 680 / 40 = 17

Therefore, C is the answer.
Answer: C
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New post 18 Apr 2018, 04:55
[GMAT math practice question]

Which of the following relationships must be inversely proportional to each other?

I. Work done and working time
II. Speed and Traveling Time
III. Profit and Cost

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

=>

Statement I
Let R be the work rate, W be the work done and T be the working time. Then R = W/T and T = W*R. Therefore, T and W are directly proportional.

Statement II
Let V be the speed, D be the distance and T be the traveling time. Then
V = D/T, and V and T are inversely proportional.

Statement III
Let P be the profit, R be the revenue and C be the cost. Then
P = R – C, and P and C are neither directly nor inversely proportional.

Therefore, B is the answer.

Answer B
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New post 19 Apr 2018, 02:49
[GMAT math practice question]

Attachment:
4.17.png
4.17.png [ 2.34 KiB | Viewed 335 times ]


The above table shows a set of scores and their frequencies. If the median score is not one of the scores displayed in the table, which of the following could be the value of x?
A. 6 B. 7 C. 8 D. 9 E. 10

=>

If x = 6, the median is 12.5.
If x = 7, 8, 9, or 10, the median is 12.

Since 12.5 is not shown on the table, the answer is 6.

Therefore, the answer is A.

Answer: A
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New post 20 Apr 2018, 01:09
[GMAT math practice question]

Alice makes 2-digit codes using the 26 letters of the alphabet. Letters may be used repeatedly, and at least one vowel must be used. How many possible codes can she make?

A. 235
B. 256
C. 360
D. 625
E. 676

=>

The number of vowels is 5 (a,e,i,o,u). So, the number of codes is equal to the number of 2-digit codes with no restrictions minus the number of codes that contain no vowels. This is given by

26*26 – 21*21 = (26 + 21)(26 – 21) = 47*5 = 235.

Therefore, the answer is A.
Answer: A
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New post 22 Apr 2018, 18:29
[GMAT math practice question]

What is the difference between the average (arithmetic mean) of the first 9 positive integers and the average (arithmetic mean) of the second 9 non-negative integers?

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

=>

The first 9 positive integers are 1, 2, 3, …, 9. Their average is 5.
The second 9 non-negative integers are 1, 2, 3, …, 9, since the first 9 non-negative integers are 0, 1, 2, …, 8. Their average is 5 too.

Thus the difference between those averages is 0.

Therefore, A is the answer.
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New post 22 Apr 2018, 18:30
[GMAT math practice question]

If the sum of the squares of two positive integers is 106, what is the sum of the two integers?

A. 13
B. 14
C. 15
D. 16
E. 17

=>

x^2 + y^2 = 106.
We can plug-in the numbers from 1 to 10 to find the values of x and y that work.
We find that 9^2 + 5^2 = 81 + 25 = 106. So, the two numbers are 5 and 9, and their sum is 9 + 5 = 14.

Therefore, the answer is B.
Answer: B
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New post 25 Apr 2018, 00:37
[GMAT math practice question]

How many 5 digit numbers have at least one zero digit?

A. 30951
B. 40141
C. 47132
D. 50001
E. 50433

=>

The number of 5 digit numbers is 99999 – 10000 + 1 = 90000.
The number of 5 digit numbers which have no 0 digit is 9 * 9 * 9 * 9 * 9 = 59049.
When we encounter the words “at least” in probability questions, we should consider the complementary case and subtract the number of ways it occurs from the total number of possibilities.
The total number of 5 digit numbers with at least one zero digit is
90000 – 59049 = 30951

Therefore, A is the answer.
Answer A
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New post 26 Apr 2018, 01:21
[GMAT math practice question]

How many possible 7-digit codes can be formed from the letters s, u, c, c, e, s, s?

A. 400
B. 420
C. 450
D. 500
E. 510

=>

The number of permutations of 7 different letters is 7!.
However, 3 of the letters are ‘s’ and 2 of the letters are ‘c’. Therefore, the number of permutations of the letters s, u, c, c, e, s, s is 7! / (3! * 2!) = 420.


Therefore, the answer is B.
Answer: B
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New post Updated on: 29 Apr 2018, 22:04
[GMAT math practice question]

Alice sells apples. She sold at least 10 lb every day last week. If the total weight of apples sold last week was 140, what is the largest possible range of the weights of apples sold on each day last week?

A. 40
B. 50
C. 60
D. 70
E. 80

=> Since the minimum weight of apples sold is 10, the greatest range occurs for the greatest maximum. The greatest maximum occurs when all but one of the weights sold is 10 lb.
If the weights are 10, 10, 10, 10, 10, 10, max, then we must have max + 10 + 10 + 10 + 10 + 10 + 10 = max + 60 = 140.
Thus, max = 80.
The range is max - min = 80 - 10 = 70.

Therefore, the answer is D.
Answer : D
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Originally posted by MathRevolution on 27 Apr 2018, 01:10.
Last edited by MathRevolution on 29 Apr 2018, 22:04, edited 1 time in total.
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New post 29 Apr 2018, 18:33
[GMAT math practice question]

The minimum of the integers x, y, and z is 10 and their average is 11. What is the greatest possible value of their maximum?

A. 10
B. 11
C. 12
D. 13
E. 14

=>

Assume x ≤ y ≤ z.
( x + y + z ) / 3 = 11 and x = 10
We have 10 + y + z = 33 or y + z = 23.
In order to have the greatest maximum number, y must be the minimum which is 10.
10 + z = 23.
z = 13.

Therefore, D is the answer.

Answer : D
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New post 02 May 2018, 03:02
[GMAT math practice question]

If the profit on a product is 20 percent of its sales price, what percent is the profit of the cost price?

A. 20%
B. 25%
C. 30%
D. 33+(1/3)%
E. 35%

=>

Let P, R and C be the profit, the sales price (revenue) and the cost price of the product, respectively.
Then P = R – C.
Since P is 20 percent of the sales price, the IVY method tells us that P = 20*(1/100)*R.
So, P = (1/5)R or R = 5P.
Plugging this into P = R – C yields P = 5P – C or C = 4P.
It follows that P = (1/4)C, and P is 25 percent of C.

Therefore, B is the answer.
Answer B
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New post 03 May 2018, 02:14
[GMAT math practice question]

Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs

=>

Suppose W is the total amount of work required to do the job and that RA and RB are the work rates of machines A and B, respectively.
Then the original condition tells us that RB = (1/2)RA.

Since machine A worked on the job for 6 hours, 1/4 of the job has been done, and (3/4)W is left.
The time T that machine B takes to complete the job is T = (3/4)W / RB = (3/4)W / (1/2)RA = (6/4)W/RA = (6/4)*24 = 36.

Therefore, the answer is E.

Answer: E
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New post 06 May 2018, 07:20
[GMAT math practice question]

The distance between Alice’s house and Bob's is 120 miles. Alice and Bob travel in opposite directions along the same road, starting at the same time. They meet at a place that is 40 miles away from Alice’s house. If Alice’s velocity is x miles per hour, what is Bob's velocity in terms of x?

A. (1/3)x
B. (1/2)x
C. x
D. 2x
E. 3x

=>

Let v be Bob’s speed, and let t be the time they take to reach their meeting point. Then
xt = 40 and vt = 120 – 40 = 80.

Bob travels 80 miles in the time it takes Alice to travel 40 miles.
Thus, Bob’s speed is twice Alice’s speed.
In terms of x, this is 2x.

Therefore, the answer is D.

Answer : D
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New post 07 May 2018, 02:25
[GMAT math practice question]

How many multiples of 4 lie between 4^4 and 4^5, inclusive?

A. 128
B. 129
C. 192
D. 193
E. 256

=>
Since we are including the end points, the number of multiples of 4 is

( 4^5 – 4^4 ) / 4 + 1 = 4^4(4-1)/4 + 1 = 4^3*3 + 1 = 64 * 3 + 1 = 193.

Therefore, D is the answer.

Answer : D
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New post 07 May 2018, 02:27
[GMAT math practice question]

If x is the sum of the first 10 positive multiples of 3 and y is the sum of the first 10 positive multiples of 2, which of the following is a factor of x – y?

A. 20
B. 35
C. 55
D. 75
E. 90

=>
x – y = ( 3 + 6 + 9 + … + 30 ) - ( 2 + 4 + 6 + … + 20 )
= 3(1 + 2 + … + 10 ) – 2( 1 + 2 + 3 + … + 10 )
= ( 3 – 2 ) ( 1 + 2 + 3 + … + 10 )
= 55
= 5 * 11

Therefore, the answer is C.
Answer: C
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New post 13 May 2018, 18:45
[GMAT math practice question]

(2^5+2^6+2^7+2^8)^2=?

A. 2^83^25^2
B. 2^{10}3^45^4
C. 2^{10}+2^{12}+2^{14}+2^{16}
D. 2^{25}+2^{36}+2^{49}+2^{64}
E. 2^{10}3^25^2

=>

(2^5+2^6+2^7+2^8)^2
= (2^5 ( 2^0 + 2^1 + 2^2 + 2^3 ))^2
= (2^5 ( 1 + 2 + 4 + 8 ))^2
= (2^5 (15))^2
= (2^5 (3*5))^2
= 2^{10}*3^2*5^2

Therefore, E is the answer.
Answer : E
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New post 13 May 2018, 18:46
[GMAT math practice question]

If the terms of a sequence {An} are defined by An=n/100, where n ranges over all the integers between 101 and 200, inclusive, what is the sum of all the An?

A. 150
B. 150.5
C. 151
D. 200
E. 201

=>
A101 + A102 + … + A200
= 101/100 + 102/100 + … + 200/100
= (1/100)( 101 + 102 + … + 200 )
= (1/100) ( 100*( 101 + 200 ) / 2 )
= 301/2 = 150.5

Therefore, the answer is B.
Answer: B
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New post 16 May 2018, 03:19
[GMAT math practice question]

For all n > 0, the nth term of the arithmetic sequence { An } may be found using the formula An=A1+(n-1)d. If A1=4 and A10= 94, what is the value of A11?

A. 101
B. 102
C. 103
D. 104
E. 105

=>

We first need to find d. Now,
A10 = A1 + 9d
=> 94 = 4 + 9d
=> 9d = 90
=> d = 10.
So,
A11 = A1 + (11-1)d = 4 + 10*10 = 104.

Therefore, D is the answer.
Answer: D
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Re: Math Revolution Approach (PS) &nbs [#permalink] 16 May 2018, 03:19

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