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The Ultimate Q51 Guide [Expert Level]

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 04 Oct 2018, 18:47
1
1
[Math Revolution GMAT math practice question]

What is the sum of the solutions of the equation (x-1)^2=|x-1|?

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

=>

(x-1)^2=|x-1|
=> |x-1|^2=|x-1|
=> |x-1|^2-|x-1|=0
=> |x-1| (|x-1|-1)=0
=> |x-1| = 0 or |x-1|-1=0
=> |x-1| = 0 or |x-1|=1
=> x-1 = 0 or x-1=±1
=> x=1 = 0 or x=1±1
=> x=1, x=0 or x=2

The sum of the solutions is 0 + 1 + 2 = 3.

Therefore, the answer is E.
Answer: E
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Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 07 Oct 2018, 18:40
[Math Revolution GMAT math practice question]

If m and n are integers, is mn an odd integer?

1) m(n+1) is even
2) (m+1)n is even

=>

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.

Modifying the question:
mn is odd only when both m and n are odd. So, the question asks if both m and n are odd.

Conditions 1) and 2), when applied together, tell us that either
both m and n are odd numbers or both m and n are even numbers.

Since we don’t have a unique solution, both conditions, taken together, are not sufficient.

Therefore, E is the answer.
Answer: E
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
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"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
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V
Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 09 Oct 2018, 19:44
[Math Revolution GMAT math practice question]

If p and q are prime numbers, is pq+1 an odd number?

1) p – q = 5
2) p = 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.

Modifying the question:
pq + 1 is odd only when pq is even. So, the question is asking whether either p or q is an even prime number. Since the only even prime number is 2, the question is asking whether p or q is equal to 2.


Condition 1):
For p – q = 5, either p or q must be even. Since the only even prime number is 2, we must have p = 7 and q = 2.
Thus, condition 1) is sufficient.

Condition 2)
Since it provides no information about q, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 10 Oct 2018, 18:46
[Math Revolution GMAT math practice question]

Five letters A, P, P, L and E are listed in a row. How many arrangements have at least one letter between the two Ps?

A. 24
B. 30
C. 36
D. 42
E. 48

=>

When we encounter “at least” in counting questions or probability questions, we should consider complementary counting.
The total number of arrangements of the 5 letters is 5!/2! (5! Counts each arrangement of the two Ps 2! times).
The number of arrangements with no letter between the two Ps is 4!.
Thus, the number of arrangements in which at least one letter lies between the two Ps is 5!/2! – 4! = 60 – 24 = 36.

Therefore, C is the answer.
Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 11 Oct 2018, 18:14
[Math Revolution GMAT math practice question]

If 3 different numbers are selected from the first 8 prime numbers, what is the probability that the sum of the 3 numbers selected is even?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/8

=>

Suppose p, q and r are prime numbers.
In order for p + q + r to be even, one of them must equal 2, since 2 is the only even prime number.
Once 2 has been selected, there are 7 prime numbers remaining from which to select 2 numbers. Thus, the number of selections in which the sum of the 3 numbers is even is 7C2 = 21.
The total number of selections is 8C3 = 56.
Thus, the probability that the sum of the three numbers is even is 21/56 = 3/8.

Therefore, the answer is E.
Answer: E
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 14 Oct 2018, 18:58
[Math Revolution GMAT math practice question]

If x^2-3x=10, what is the value of x?

1) x^2-4 = 0
2) x<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.


The original condition x2-3x=10 is equivalent to x = -2 or x = 5 as shown below:

x^2-3x=10
=> x^2-3x-10= 0
=> (x+2)(x-5) = 0
=> x = -2 or x = 5

Condition 1)
x^2-4 = 0
=> (x-2)(x+2) = 0
=> x = -2 or x = 2
Only x = -2 also satisfies the original condition, so we have a unique solution.
Thus, condition 1) is sufficient.



Condition 2)
Since x < 6 from condition 2) and x = -2 or x = 5 from the original condition, x = -2 or x = 5.
Since we don’t have 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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 15 Oct 2018, 18:26
[Math Revolution GMAT math practice question]

If x=0.abcabc........(a repeating infinite decimal), what is the value of a+b+c?

1) 1-x=0.123123123…….
2) 0.8<x<0.9

=>
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 4 variables (x, a, b and c) and 1 equation (x = 0.abcabc….), E is most likely to be the answer. However, condition 1) includes 3 hidden equations (matching the values of the decimal places) and allows us to determine the values of all four variables as follows:
x = 1 – 0.123123123… = 0.876876876… = 0.abcabcabcabc…
Thus a = 8, b = 7, c = 6 and a + b + c = 8 + 7 + 6 = 21.
Condition 1) is sufficient.

Condition 2)
If x = 0.811811811…, then a = 8, b = 1, c = 1 and a + b + c = 10.
If x = 0.812812812…, then a = 8, b = 1, c = 2 and a + b + c = 11.
Since we don’t have a unique solution, condition 2) is not sufficient.


Therefore, A is the answer.
Answer: A
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6375
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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New post 16 Oct 2018, 18:14
[Math Revolution GMAT math practice question]

When A and B are positive integers, is AB a multiple of 4?

1) The greatest common divisor of A and B is 6
2) The least common multiple of A and B is 30

=>

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.

Asking if AB is a multiple of 4 is equivalent to asking if AB = 4k for some integer k.

Condition 1)
Since A = 6a = 2*3*a and B = 6b = 2*3*b for some integers a and b, AB = 2^2*3^2*ab = 4*3^2ab.
Thus, AB is a multiple of 4 and condition 1) is sufficient.

Condition 2)
If A = 6 and B = 5, then lcm(A,B) = 30, but AB = 30 is not a multiple of 4, and the answer is ‘no’.
If A = 6 and B = 10, then lcm(A,B) = 30, and AB = 60 is a multiple of 4. The answer is ‘yes’.
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: The Ultimate Q51 Guide [Expert Level] &nbs [#permalink] 16 Oct 2018, 18:14

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