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Overview of GMAT Math Question Types and Patterns on the GMAT

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New post 16 Jul 2019, 17:31
[GMAT math practice question]

(Statistics) A class consists of 30 students. Among them a students have 90 books, b students have 80 books, c students have 70 books and all the remaining students have 60 books. What is the average number of books the students in the class have?

1) a= b+c
2) a is twice b

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (a, b and c) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

The average number of books is
( 90a + 80b + 70c +60(30 – a – b – c) ) / 30
= ( 30a + 20b + 10c + 1800) /30

If a = 2, b = 1 and c = 1, then the average is (60 + 20 + 10 + 1800)/30 = 1890/30 = 63.
If a = 4, b = 2 and c = 2, then the average is (120 + 40 + 20 + 1800)/30 = 1980/30 = 66.

Since both conditions together don’t yield a unique solution, they are not sufficient.
Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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New post 17 Jul 2019, 17:25
[GMAT math practice question]

(arithmetic) What is 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56?

A. 3/5
B. 5/8
C. 7/8
D. 8/9
E. 9/10

=>

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56
= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) + 1/(6*7) + 1/(7*8)
= (1/1 – 1/2) + (1/2 – 1/3) + (1/3 – 1/4) + (1/4 – 1/5) + (1/5 – 1/6) + (1/6 – 1/7) + (1/7 – 1/8)
= 1/1 – 1/8 = 7/8

Therefore, C is the answer.
Answer: C
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New post 18 Jul 2019, 17:38
[GMAT math practice question]

(ALGEBRA) As the figure shows, A = -5 and B = 4. If AC:CD:DB=1:2:3, what are the values of C and D?

A. -3 and -1
B. -3.5 and -0.5
C. -2.5 and 0.5
D. 1 and 3
E. 0 and 1

Attachment:
7.12.png
7.12.png [ 1.64 KiB | Viewed 362 times ]


=>

Since AC:CD:DB = 1:2:3, we can put AC = k, CD = 2k and DB = 3k.
Then k + 2k + 3k = 6k = 4 – (-5) = 9 and k = 3/2.
Thus, C = A + k = -5 + (3/2) = -(7/2) = -3.5 and D = B – 3k = 4 – 9/2 = -(1/2) = -0.5.

Therefore, B is the answer.
Answer: B
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New post 21 Jul 2019, 17:48
[GMAT math practice question]

(algebra) What is a?

1) 3x-[7x-{2x-(5-6x)}] = -10x+4
2) –a+5 = 11x

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (a and x) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) and 2)
3x-[7x-{2x-(5-6x)}] = 3x-[7x-{2x-5+6x}] = 3x-[7x-{8x-5}] = 3x-[7x-8x+5] = 3x-[-x+5] = 3x+x-5 = 4x – 5 = -10x + 4
Then, by condition 1), we must have 14x = 9 and x = 9/14.
Since –a + 5 = 11x, we have a = 5 -11x = 5 -11(9/14) = -(29/14)
Thus, both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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New post 22 Jul 2019, 17:53
[GMAT math practice question]

(algebra) Let x be a real number. (a, b) denotes ax+b. What is (1, 0)?

1) 3*(2,0)=(-1, 4) – (-2, -6)
2) (1, 0)^2 +4 = 4(1, 0)

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Since (1, 0)=1*x+0=x, the question asks for the value of x.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
The left hand side is 3*(2,0) = 3*(2x + 0) = 6x and the right hand side evaluates to (-1,4) – (-2,-6) = -x + 4 – (-2x – 6) = x + 10. Equating both sides yields 6x = x + 10 and x = 2.
Thus, condition 1) is sufficient.

Condition 2)
(1,0)^2 + 4 = 4(1,0)
=> (x)^2 + 4 =4(x)
=> x^2 -4x + 4 = 0
=> (x-2)^2 = 0
=> x = 2.
Thus, condition 2) is also sufficient.

Therefore, D is the answer.
Answer: D

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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New post 23 Jul 2019, 17:58
[GMAT math practice question]

(ratio) Tom painted 1/3 of a wall red, 1/5 of the wall blue and the remaining 238 m^2 black. What is the area of the wall in m2?

A. 490
B. 500
C. 510
D. 520
E.530

=>

Using the Ivy Approach, we assume 15w is the area of the wall. We have chosen 15 since it is the lcm of the denominators, 3 and 5. So, 15w/3 = 5w is the area painted red, and 15w/5 = 3w is the area painted blue.
The area painted black is given by the equation
15w-(15w·1/3)-(15w·1/5)=15w-5w-3w=7w=238.

Solving for w yields w=34. So, the area of the whole wall is 15w=15·34=510 m^2.

Therefore, C is the answer.
Answer: C
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New post 25 Jul 2019, 17:33
[GMAT math practice question]

(speed) Tom travels from A to B at a constant speed of 4 miles per hour and returns from B to A at a constant speed of 8 miles per hour. What is Tom’s average speed for the entire journey?

A. 14/3
B. 5
C. 16/3
D. 17/3
E. 18/3

=>

The average speed is calculated by dividing the total distance by the total time. We often encounter this type of question on the GMAT exam.

Let d be the distance between A and B.
The time that Tom takes to travel from A to B is d/4 and the time that he takes to travel from B to A is d/8.
The total time taken is (d/4) + (d/8) = 3d/8.
The average speed is 2d / (3d/8) = 16/3.

Therefore, the answer is C.
Answer: C
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New post 26 Jul 2019, 23:10
Example 9:
Stations M and N are connected by two separate, straight and parallel rail lines that are 500 miles long. Freight train A and freight train B simultaneously left Station M and Station N, respectively, and each freight train traveled to the other’s point of departure. The two freight trains passed each other after traveling for 4 hours. When the two freight trains passed, which train was nearer to its destination?

(1) At the time when the two freight trains passed, freight train A had averaged a speed of 60 miles per hour.
(2) Freight train B averaged a speed of 130 miles per hour for the entire trip.

Spoiler: :: Answer
Answer: E


How come the answer to this question is not A?
It is clear that A traveled 4 hours with 60 kmph speed so it covered a distance of 240 miles. that means, 500-240=260.
A is 260 miles away from its destination.

Also if B passed or met A exactly after 4 hours, B must have traveled at least 260 kms which means it is just
(500-260=240)
240 kms away from its destination.
Doesn't this answer our question that Train B is nearer to its destination???

Please Reply, i am a bit confused.
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New post 28 Jul 2019, 17:16
[GMAT math practice question]

(geometry) In the figure, lines AB, CD and EF are parallel, and lines BC and DE are parallel. What is the length of CD?

Attachment:
7.23.png
7.23.png [ 14.87 KiB | Viewed 225 times ]


1) AB=3
2) EF=12


=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Triangles ABC and CDE are similar, and triangles BDC and DFE are similar. So, we can set up the proportion AB:CD = CD:EF.
Since CD^2 = AB*EF, conditions 1) and 2) together give us sufficient information to calculate the value of CD.

Therefore, C is the answer.
Answer: C

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New post 29 Jul 2019, 17:22
[GMAT math practice question]

(number properties) a and b are positive integers. What is the remainder when b is divided by 4?

1) if a is divided by 4, the remainder is 3
2) if a^2+b is divided by 4, the remainder is 1

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (a and b) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Condition 1) tells us that a has remainder 3, when it is divided by 4. So, a^2 has remainder 1, when it is divided by 4.
Condition 2) tells us that a^2+b has remainder 1 when it is divided by 4. Since a^2 has remainder 1 when it is divided by 4, b has remainder 0 when it is divided by 4.
Thus, both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since there is no information about b in condition 1), it is not sufficient.

Condition 2)
If a = 1 and b = 4, then b has remainder 0 when it is divided by 4.
If a = 4 and b = 1, then b has remainder 1 when it is divided by 4.
Condition 2) is not sufficient since it does not yield a unique answer.

Therefore, C is the answer.
Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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New post 31 Jul 2019, 17:07
[GMAT math practice question]

(speed) A river flows with a constant speed of 2 miles per hour. It takes 3 hours for a ship to go 6 miles upstream. How many hours does it take the ship to travel the same distance downstream?

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

=>

Assume v is the speed of the ship.
Then 6 / ( v – 2 ) = 3 and 2 = v – 2. Thus, v = 4.
The number of hours it takes for the ship to go 6 miles downstream, is 6 / ( v + 2 ) = 6 / ( 4 + 2 ) = 1.

Therefore, D is the answer.
Answer: D
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New post 01 Aug 2019, 17:14
[GMAT math practice question]

(geometry) ABCD is a square with AB=10. What is the perimeter of the shaded area?

Attachment:
7.25ps.png
7.25ps.png [ 14.82 KiB | Viewed 574 times ]


A. 10π/3 +10
B. 5π/3 +10
C. 5π/6 +10
D. 5π/3 +5
E. 5π/6 +5

=>

Attachment:
7.29ps.png
7.29ps.png [ 8.99 KiB | Viewed 574 times ]


Since triangle PBC is equilateral, angle ABP has measure 30° and the length of arc AP is 2π*10*(30/360) = (5/3) π.
Thus, the perimeter of the shaded area is (5/3) π *2 + 10 = (10/3) π + 10.

Therefore, A is the answer.
Answer: A
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New post 04 Aug 2019, 18:01
[GMAT math practice question]

(number properties) n is a positive integer. What is the value of n?

1) n+200 is a perfect square
2) n+292 is a perfect square

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
If n + 200 = 400 = 20^2, then n = 200.
If n + 200 = 441 = 21^2, then n = 241.
Since condition 1) does not yield a unique answer, it is not sufficient.

Condition 2)
If n + 292 = 400 = 20^2, then n = 108.
If n + 292 = 441 = 21^2, then n = 149.
Since condition 2) does not yield a unique answer, it is not sufficient.

Conditions 1) & 2)
Write n + 200 = a^2 and n + 292 = b^2, for some positive integers a and b. Then
b^2 – a^2 = (n+292)-(n+200) = 92 = 2^2*23 and
(b+a)(b-a) = 2^2*23

Since b + a and b – a have the same parity, which means both b + a and b – a are even or both b + a and b – a are odd, b + a = 46 and b – a = 2.
Solving these equations simultaneously yields a = 22 and b = 24.
Thus n = 24^2 – 292 = 284.
The two conditions are sufficient, when applied together.

Therefore, C is the answer.
Answer: C

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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New post 05 Aug 2019, 12:44
MathRevolution, I agree with chetan2u - question 1 is poorly written. There is no way this would appear on an actual GMAT, there are numerous grammatical errors.

Quote:
On a certain transatlantic crossing, 40 percent all passengers held round-trip tickets. [............] what percent of the ship’s passengers held round-trip tickets?


You can ignore everything in the middle, and get the answer.

Here's how the question was probably trying to be formulated:

On a certain transatlantic crossing, 40 percent of all passengers held round-trip tickets and also took their laptops aboard the ship. If 20 percent of the passengers with round-trip tickets did not take their laptops aboard the ship, what percent of the ship’s passengers held round-trip tickets?
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New post 06 Aug 2019, 17:23
[GMAT math practice question]

(algebra) What is the value of (a-b)/(a+b) –ab + b/c ?

1) a=bc
2) a=1/2

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Plugging in a = bc = 1/2 yields
(a-b)/(a+b) – ab + b/c = (bc-b)/(bc+b) – b^2c + b/c = b(c-1) / b(c+1) – (1/2)c + (bc)/c^2 = (c-1)/(c+1) – 1/2c + 1/(2c^2).
Since we don’t know the value of c, both conditions together don’t yield a unique solution and they are not sufficient.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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New post 12 Aug 2019, 00:10
[GMAT math practice question]

(algebra) What is the value of (3mr-nt)/(4nt-7mr)?

1) m/n = 4/3
2) r/t= 9/14

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.


The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify the conditions if necessary.

We rearrange (3mr-nt)/(4nt-7mr) to see if we can write in terms of the ratios m/n and r/t given in the conditions:
(3mr-nt)/(4nt-7mr)
= ( (3mr)/(nt) – (nt/nt) ) / ( 4(nt/nt) – 7mr/nt )
= ( 3(m/n)*(r/t) – 1 ) / ( 4 – 7(m/n)(r/t) )

Now, both conditions 1) & 2) together are sufficient since the simplified question requires only the values of (m/n) and (r/t).

Therefore, C is the answer.
Answer: C
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New post 13 Aug 2019, 17:50
[GMAT math practice question]

(function) For which value of x will y=ax^2+20x+b have a minimum in the xy-plane?

1) b=10
2) a=2

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the numbers of variables and equations.

We can modify the original condition and question as follows:

If a > 0, the function will have a minimum at x = (-20)/(2a) = (-10)/a.
If a < 0, the function has no minimum. So, to answer the question, we need to find the value of a.
Thus, condition 2) is sufficient.

Note: condition 1) cannot be sufficient as it provides no information about the value of a.

Therefore, the answer is B.
Answer: B
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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New post 18 Aug 2019, 17:39
[GMAT math practice question]

(Number) What is the units digit of 3^n?

1) n is a multiple of 4
2) n is a multiple of 6

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify the conditions if necessary.

The units digits of 3^n for n = 1, 2, 3, 4, … are 3, 9, 7, 1, 3, 9, 7, 1, …
So, the units digits of 3^n have period 4:
They form the cycle 3 -> 9 -> 7 -> 1.
Thus, 3^n has a units digit of 1 if n is a multiple of 4.

Note that 6 is not a multiple of 4.

Therefore, A is the answer.
Answer: A
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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New post 19 Aug 2019, 17:40
[GMAT math practice question]

(number properties) What is the remainder when 1+n+n^2 +…+ n^8 is divided by 5?

1) The remainder when n is divided by 5 is 3
2) n is less than 5

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The easiest way to solve remainder questions is to plug in numbers.
The units digits of 3^n for n = 1, 2, 3, 4, … are 3, 9, 7, 1, 3, 9, 7, 1, …
So, the units digits of 3^n have period 4:
They form the cycle 3 -> 9 -> 7 -> 1.
Thus, if n has remainder 3 when it is divided by 5, 1+n+n^2 +…+ n^8 has the same remainder as 1 + 3 + 9 + 7 + 1 + 3 + 9 + 7 + 1 = 21 when it is divided by 5. It has a remainder of 1 when it is divided by 5.
Condition 1) is sufficient.

Condition 2)
If n = 1, then 1+n+n^2 +…+ n^8 = 9, which has remainder 4 when it is divided by 5.
If n = 3, then 1+n+n^2 +…+ n^8 has remainder 1 when it is divided by 5.
Since condition 2) doesn’t yield a unique solution, it is not sufficient.

Therefore, A is the answer.
Answer: A
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Math Revolution GMAT Instructor
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GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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New post 21 Aug 2019, 17:39
[GMAT math practice question]

(Statistics) When playing a coin-tossing game, Tom wins $5 when the coin lands on heads and loses $3 when the coin lands on tails.
After tossing the coin 20 times Tom has won a total of $12. How many times did the coin land on heads?

A. 7
B. 8
C. 9
D. 10
E. 11

=>

Let h be the number of times the coin landed on heads.
Then 20 – h is the number of times the coin landed on tails.
Thus, Tom won 5h – 3(20-h) = 8h – 60 dollars.
Since Tom won $12, this gives the equation 8h - 60 = 12. Solving this equation yields 8h = 72 and h = 9.

Therefore, C is the answer.
Answer: C
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 21 Aug 2019, 17:39

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