The Ultimate Q51 Guide [Expert Level]

[Math Revolution GMAT math practice question]

3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between 10 and 200, inclusive?

A. 54
B. 57
C. 60
D. 63
E. 66

=>

12 is the smallest multiple of 3 and 198 is the largest multiple of 3 between 10 and 200, inclusive.
Thus, the number of multiples of 3 between 10 and 200, inclusive is ( 198 – 12 ) / 3 + 1 = 186/3 + 1 = 62 + 1 = 63

Therefore, the answer is D.
Answer: D

[Math Revolution GMAT math practice question]

The four-digit number 486X, where X is the units digit of 486X, is a multiple of 36. What is the value of X?

A. 0
B. 2
C. 4
D. 6
E. 8

=>

Since X is a one-digit integer, 0 ≤ X ≤ 9.
36 = 4*9, so 486X is a multiple of both 4 and 9.
Since 486X is a multiple of 4, 6*10 + X must be a multiple of 4.
Thus, X is one of values 0, 4 and 8.
In addition, since 486X is a multiple of 9, the sum of all of its digits, 4 + 8 + 6 + X = X + 18 is a multiple of 9.
Thus, X must be 0 or 9.

0 is the only one of these digits for which 486X is a multiple of 36.

Therefore, the answer is A.
Answer: A

Thanks ..its a really informative thread

[Math Revolution GMAT math practice question]

Is x^2>xy?

1) x>y
2) y>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.
x^2>xy
=> x^2-xy > 0
=> x(x-y) > 0
=> x>0, x>y or x<0, x<y

Since we have 2 variables (x and y) 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)
Since we have x > y and x > 0 from x > y > 0 which are a combined inequality of both conditions, both conditions together are sufficient.

Since this question is an inequality 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) x > y
If x = 2, y = 1, then we have x^2>xy and the answer is ‘yes’.
If x = -1, y = -2, then we have x^2<xy and the answer is ‘no’.

Condition 2) y > 0
If x = 2, y = 1, then we have x^2>xy and the answer is ‘yes’.
If x = 1, y = 2, then we have x^2<xy and the answer is ‘no’.


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.

[Math Revolution GMAT math practice question]

Machine A takes 20 minutes and B takes 15 minutes to warm up. The machine A produces 300 pins per 1 minute and the machine B produces 200 parts per 1 minute. Including the time for warming up, is the number of pins produced by machine A smaller than the number of pins from the machine B?

1) The number of pins is greater than 3000
2) The number of pins is less than 4000

=>

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.

Let w be the number of pins.
20 + w / 300 is the time the machine A takes to produce w pins and 15 + w / 200. The question asks if 20 + w / 300 is less than 15 + w / 200.
20 + w / 300 < 15 + w / 200
=> 5 < w/200 – w/300
=> 5 < 3w/600 – 2w/600
=> 5 < w/600
=> 3000 < w

Since condition 1) is same as the question, condition 1) is sufficient.

Condition 2)
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
The solution set 3000 < w of the question does not include the solution set of condition 2) w < 400. Thus condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

[Math Revolution GMAT math practice question]

If n is contained in the set A, n+5 is contained in set A. Is 50 contained in set A?

1) 30 is contained in the set A.
2) 100 is contained in the set S

=>

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.

Condition 1)
Since 30 is in the set A, 35, 40, 45, 50 are in the set A.
Condition 1) is sufficient.

Condition 2)
A = { 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, … }
The set A has 40.
But the set A = { 100, 105, 110, … } does not have 40.
Condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

[Math Revolution GMAT math practice question]

| 1 - | 2 - | 3 - | 4 – π | | | |

A. π
B. π - 1
C. π - 2
D. π - 3
E. 4 - π

=>

| 1 - | 2 - | 3 - | 4 – π | | | |
= | 1 - | 2 - | 3 – ( 4 – π ) | | |
= | 1 - | 2 - | π - 1 | | |
= | 1 - | 2 – ( π - 1 ) | |
= | 1 - | 3 – π | |
= | 1 – ( π - 3 ) |
= | 4 – π |
= 4 – π

Therefore, the answer is E.
Answer: E

[Math Revolution GMAT math practice question]

A car and a bicycle traveled in the same direction along the equal route at their constant speed rates of 40 miles per hour and 30 miles per hour, respectively. After 15 minutes the car passed the bicycle, the car reaches a waiting point, how long it takes the bicycle to reach the waiting point?

A. 15 min
B. 20 min
C. 25 min
D. 30 min
E. 35 min

=>

Since the car traveled for 15 minutes with the speed 40 mph, it moved 10 miles. It take 20 minutes the bicycle to travel 10 miles with the speed 30 mph.

Therefore, the answer is B.
Answer: B

Is this not a relative speed problem? Because when the car passes the bicycle, the bicycle is still moving. So their relative speed is 40 - 30 = 10.

The car travels for 15 minutes, or 10 x 1/4 = 5/2 miles, and stops.

Bicycle takes 5/2x1/30 = 1/12 hours = 5 minutes to catch up. Am I going wrong somewhere? Because the question doesn't say the bicycle stops after the car passes it.

[Math Revolution GMAT math practice question]

What is the value of f(10)?

1) f(x) = 2 for 0 ≤ x < 3
2) f(x+3) = 2f(x)

=>

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.

When asked about a function, we assume there are many variables so that E is most likely to be the answer.

Conditions 1) & 2):
Repeatedly applying condition 2) gives f(10) = 2f(7), f(7) = 2f(4) and f(4) = 2f(1), so that f(10) = 2f(7) = 4f(4) = 8f(1).
Since f(1) = 2 by condition 1), f(10) = 8*2 = 16.
Both conditions together are sufficient.

It is easy to see that neither condition is sufficient on its own.

Therefore, C is the answer.
Answer: C

[Math Revolution GMAT math practice question]

Is |x|/x equal to -1?

1) x>0
2) x<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.

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

The question |x|/x = -1 is equivalent to x ≤ 0 as shown below:
|x|/x = -1
=> |x| = -x
=> x ≤ 0

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

Condition 1)
If x > 0, then “x ≤ 0” is always false, and the answer is ‘no’.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
Condition 2) is not sufficient, since the solution set of the question does not include the solution set of condition 2).

Therefore, A is the answer.
Answer: A

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.

[Math Revolution GMAT math practice question]

Is the 5-digit positive integer abc000 divisible by 24?

1) The 3-digit integer abc is divisible by 8.
2) The 3-digit integer abc is divisible by 3.

=>

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.

Since the last three digits 000 is a multiple of 8 and abc000 is a multiple of 8, the question “is abc000 divisible by 24?” is equivalent to “is abc000 divisible by 3?” or “is a + b + c divisible by 3?”.
Thus, condition 2) is sufficient.

Condition 1) is not sufficient as 8 is not divisible by 3.

Therefore, the correct answer is B.
Answer: B

[Math Revolution GMAT math practice question]

If f(x)=x^2 when x<0 and f(x)=x when x≥0, what is the value of f(a)?

1) |a|=1
2) a2-a = 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.

Since we have 1 variable (a) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
|a| = 1 => a = ±1.
If a = 1, then f(a) = f(1) = 1.
If a = -1, then f(a) = f(-1) = (-1)^2 = 1.
Since it gives a unique solution, condition 1) is sufficient.

Condition 2)
a2 - a = 0 => a(a-1) = 0 => a=0 or a =1
If a = 0, then f(a) = f(0) = 0.
If a = 1, then f(a) = f(1) = 1.
Since it does not give a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

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.

[Math Revolution GMAT math practice question]

If xy≠0 and x^2+4y^2=4xy, (x+y)/(x-y)=?

A. 1
B. √2
C. √3
D. 2
E. 3

=>

x^2+4y^2=4xy
=> x^2-4xy+4y^2=0
=> (x-2y)^2=0
=> x=2y

Thus, (x+y)/(x-y) = (2y+y)/(2y-y) = 3y/y = 3.

Therefore, E is the answer.
Answer: E

[Math Revolution GMAT math practice question]

If n is an integer between 30 and 50 inclusive, what is the value of n?

1) When n is divided by 8, the remainder is 7
2) When n is divided by 16, the remainder is 7

=>

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)
We can express n = 8k+7 for some integer k.
If k = 3, then n = 31.
If k = 4, then n = 39.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
We can express n = 16m+7 for some integer m.
If m = 2, then n = 39.
If m = 1, then n = 23 and n < 30.
If m = 3, then n = 55 and n > 50.
Thus n = 39 is the unique solution and condition 2) is sufficient.

Therefore, B is the answer.
Answer: B

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.

[Math Revolution GMAT math practice question]

If n is an integer greater than 1, what is the value of n?

1) n is a prime number
2) (n+2)/n is an integer

=>

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 of the conditions on their own first.

Condition 1)
Since there are many prime numbers, condition 1) is not sufficient.

Condition 2)
If n = 1, then (n+2)/n = 3 is an integer.
If n = 2, then (n+2)/n = 2 is an integer.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If n = 2, then (n+2)/n = 2 is an integer.
If n = 3, then (n+2)/n = 5/2 is not integer.
If n is a prime number bigger than 2, (n+2)/n is not an integer.
Thus n = 2 is the unique solution and both conditions together are sufficient.

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.

[Math Revolution GMAT math practice question]

Is x^3-4x>0？

1) x>2
2) x>-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. We then recheck the question.

x^3-4x>0
=> x(x^2-4)>0
=> x(x+2)(x-2)>0
=> -2<x<0 or x > 2

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

Condition 1)
In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
Since the solution set of the question, -2<x<0 or x > 2, includes the solution set of condition 1), x > 2, condition 1) is sufficient.

Condition 2)
The solution set of the question, -2<x<0 or x > 2, does not include the solution set of condition 2), x > -2, so condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

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.