GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 06 Jul 2020, 10:22

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The Ultimate Q51 Guide [Expert Level]

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 10 Feb 2019, 17:16
[GMAT math practice question]

If x, y are integers, is (x-y)(x+y)(x^2+y^2) an odd number?

1) x is an odd number
2) x-y is an odd number

=>

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 (x-y)(x+y)(x^2+y^2) = x^4-y^4, the question asks if x and y have different parities.

By Condition 2), x and y must have different parities since x – y is an odd number.
Condition 2) is sufficient.

Condition 1)
Since we don’t know whether y is even or odd, condition 1) is not sufficient.

Therefore, B is the answer.
Answer: B
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 11 Feb 2019, 17:26
[GMAT math practice question]

If x, y, z are positive integers, is xyz64?

1) xy≥yz≥zx≥16
2) x+y+z=64

=>

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, z) and 0 equations, E is most likely to be the answer. So, we should consider each condition on its own first. As condition 1) includes 3 equations, we should consider it first.

Condition 1)
Since xy ≥ 16, yz ≥ 16, and zx ≥ 16, we have (xyz)^2 ≥ 16^3 or xyz ≥ 64.
Condition 1) is sufficient.

Condition 2)
If x = 20, y = 20 and z = 24, then xyz = 9600 ≥ 64 and the answer is ‘yes’.
If x = 1, y = 1 and z = 62, then xyz = 62 < 64 and the answer is ‘no’.
Since condition 2) does not yield a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

This is a CMT(Common Mistake Type) 4(A) question. If a question is from one of the key question areas and C should be the answer, CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 12 Feb 2019, 17:27
[GMAT math practice question]

3x+4y=?

1) 2|x|+3|y|=0
2) 3|x|+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.

Condition 1)
Since |x| ≥ 0, |y| ≥ 0 and 2|x| + 3|y| = 0, we have x = y = 0.
Therefore, 3x + 4y = 0.
Condition 1) is sufficient.

Condition 2)
Since |x| ≥ 0, |y| ≥ 0 and 3|x| + 2|y| = 0, we have x = y = 0.
Therefore, 3x + 4y = 0. Condition 2) is sufficient.

FYI: Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, the answer is D.
Answer: D
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 13 Feb 2019, 17:21
[GMAT math practice question]

Does f(x)=ax^4+bx^3+cx^2+dx+e have (x-2) as a factor?

1) f(2)=0
2) f(-2)=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.
The statement that f(x)=ax^4+bx^3+cx^2+dx+e has (x-2) as a factor is equivalent to saying f(x) = (x-2)g(x) for some function g(x). This is equivalent to the requirement that f(2) = 0.

Thus condition 1) is sufficient.

Condition 2)
If f(x) = (x-2)(x+2)(x-1)(x+1), then f(x) has x-2 as a factor, The answer is ‘yes’.
If f(x) = x(x+2)(x+1)(x-1), then f(x) doesn’t have x-2 as a factor. The answer is ‘no’.
Since condition 2) does not yield a unique answer, condition 2) is not sufficient.

Therefore, the answer is A.
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 14 Feb 2019, 17:29
[GMAT math practice question]

If (x-7)^2=-|y-5|, xy=?

A. 5
B. 7
C. 12
D. 35
E. cannot be determined

=>

(x-7)^2=-|y-5|
=> (x-7)^2+|y-5| = 0
=> x = 7 and y = 5
This yields xy = 35.

Therefore, the answer is D.
Answer: D
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

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

What is the area of a right triangle?

1) The length of one side is 3
2) The length of one side is 4

=>

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 questions about triangles involve three variables, E is most likely to be the answer.

Conditions 1) & 2)
If the sides given are legs, then the area of the right triangle is (1/2)*3*4 = 6.
If one leg has length 3 and the hypotenuse has length 4, then, by Pythagoras’ theorem, the length of the other leg is √(4^2 – 3^2) = √7, and the area of the triangle is (1/2)*3*√7 =(3√7)/2.
Thus, both conditions together are not sufficient, since they do not yield a unique solution.

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.
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 18 Feb 2019, 17:35
[GMAT math practice question]

x^3-y^3=?

1) x-y=0
2) |x|=|y|

=>

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-y^3 = (x-y)(x^2+xy+y^2)

Condition 1)
If x – y = 0, then x^3-y^3 = (x-y)(x^2+xy+y^2) = 0.
Thus, condition 1) is sufficient.

Condition 2)
If x = 1 and y = 1, then x^3-y^3 = 1 – 1 = 0.
If x = 1 and y = -1, then x^3-y^3 = 1 –(-1) = 2.
Condition 2) is not sufficient since it does not yield a unique solution.

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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 19 Feb 2019, 17:27
[GMAT math practice question]

How many numbers between 1 and 200, inclusive, have a 2 in the units place and are divisible by 4?

A. 8
B. 9
C. 10
D. 11
E. 12

=>

In order for a number with 2 in the units place to be divisible by 4, the last two digits must be one of 12, 32, 52, 72 and 92.
Thus, the numbers between 1 and 200, inclusive, satisfying this property are
12, 32, 52, 72, 92, 112, 132, 152 and 172.

There are 8 such numbers. 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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 20 Feb 2019, 17:27
[GMAT math practice question]

How many integers between 18 and 3399 are multiples of 17?

A. 198
B. 199
C. 200
D. 201
E. 202

=>

18 = 17*1 + 1, 34 = 17*2 is the least multiple of 17 greater than 18.
3399 = 17*199 + 16, 3383 = 17*199 is the greatest multiple of 17 less than 3399.
Thus, the multiples of 17 between 18 and 3399 are 34=17*2, … , 3383 = 17*199. There are 198 = (199 – 2) + 1 of these numbers as they are in one-to-one correspondence with the integers between 2 and 199, inclusive.

Therefore, the answer is A.
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

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

What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})?

A. 3/5
B. 5/3
C. 2^{2018}
D. 2^{2019}
E. 2^{2020}

=>

(2^{2020} + 2^{2018}) / (2^{2020}-2^{2018})
= (2^22^{2018} + 2^{2018}) / (2^22^{2018}-2^{2018})
= (2^{2018})(2^2+1) / (2^{2018})(2^2-1) = (2^2+1) / (2^2-1)
= 5/3

Therefore, the answer is B.
Answer: B
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 24 Feb 2019, 17:27
If a and b are integers, and x and y are positive integers, is ax+by >0?

1) ax+y>0
2) bx+y>0

Answer: E

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 (a, b, x and y) 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):
If a = 1, b = 1, x = 1 and y = 1, then a^x+b^y = 2, and the answer is ‘yes’.
If a = -1, b = -1, x = 1 and y = 1, then a^x+b^y = -2, and the answer is ‘no’.

Thus, both conditions together are not sufficient since they do not yield a unique solution.

Therefore, E is the answer.

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.
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 25 Feb 2019, 23:16
If a and b are positive integers, is a+b divisible by 7?

1) a – b is divisible by 7
2) a+b+7 is divisible by 91

Answer: 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.

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

Condition 2) tells us that a + b + 7 = 91k for some integer k, and so a + b = 91k – 7 = 7(13k-1). Therefore, a + b is a multiple of 7.
Thus, condition 2) is sufficient.

Condition 1)
If a = 14 and b = 7, then a + b = 21 is a multiple of 7, and the answer is ‘yes’.
If a = 8 and b = 1, then a + b = 9 is not a multiple of 7, and the answer is ‘no’.
Thus, condition 1) is not sufficient since it does not yield a unique solution.

Therefore, B is the answer.
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 27 Feb 2019, 04:07
a, b, and c are positive integers. Is a+b+c an odd number?

1) ab is an odd number
2) c is an odd number

Answer: C

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 (a, b, x and y) 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 with the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Condition 1), ab is an odd integer, is equivalent to the statement that both a and b are odd numbers.
As c is also an odd number, a + b + c is an odd number since it is the sum of three odd numbers.

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)
If a = 1, b = 1, and c = 1, then a + b + c = 3 is an odd number, and the answer is ‘yes’.
If a = 1, b = 1, and c = 2, then a + b + c = 4 is not an odd number, and the answer is ‘no’.
Thus, condition 1) is not sufficient.

Condition 2)
If a = 1, b = 1, and c = 1, then a + b + c = 3 is an odd number, and the answer is ‘yes’.
If a = 2, b = 1, and c = 1, then we have a + b + c = 4 is not an odd number, and the answer is ‘no’.
Thus, condition 2) is not sufficient.

Therefore, C is the answer.

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.
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 28 Feb 2019, 06:10
A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 blue balls, 9 white balls, and 11 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 7 balls of the same color are drawn?

A. 7
B. 14
C. 15
D. 27
E. 28


Answer: E

The maximum number of draws without 7 balls of a single color is 1 + 3 + 5 + 6 + 6 + 6 = 27, obtained by drawing 1 red ball, 3 green balls, 5 yellow balls, 6 blue balls, 6 white balls and 6 black balls. If we draw one more ball, then we must have 7 balls of one color.
Thus, we need to draw 28 balls to ensure that 7 balls of the same color are drawn. Therefore, E is the answer.
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 28 Feb 2019, 20:47
[GMAT math practice question]

What is the largest digit n for which the number 123,45n is divisible by 3?

A. 3
B. 5
C. 6
D. 7
E. 9

=>

Recall that a number is divisible by 3 if and only if the sum of its digits is divisible by 3. The sum of the digits of 123,45n is 1 + 2 + 3 + 4 + 5 + n = n + 15. This is divisible by 3 exactly when n is divisible by 3.
So, n must be a multiple of 3.
Thus, the largest digit, n is 9.

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.
"Only $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 04 Mar 2019, 17:32
[GMAT math practice question]

n is a positive integer. What is the remainder when n is divided by 3?

1) n^2 has remainder 1 when it is divided by 3
2) n has remainder 7 when it is divided by 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 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)
n could be any of the integers 1, 2, 4, 5, 7, 8, …
If n is one of 1, 4, 7, then n has a remainder 1 when it is divided by 3.
If n is one of 2, 5, 8, then n has a remainder 2 when it is divided by 3.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Condition 2)
n = 9k +7 can be expressed as n = 9k + 7 = 9k + 6 + 1 = 3(3k+2)+1. Therefore, n has remainder 1 when it is divided by 3.
Thus, condition 2) is sufficient.

Therefore, B is the answer.
Answer: B
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 05 Mar 2019, 17:27
[GMAT math practice question]

Is x = y?

1) x ≤ y
2) |x| ≥ |y|

=>

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 (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)
If x =1, and y = 1, then x and y satisfy both conditions, and the answer is “yes” since x = y.
If x = -2, and y = 1, then x and y satisfy both conditions, but the answer is “no” since x ≠ y.

Thus, both conditions together are not sufficient, since they do not yield a unique solution.

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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 06 Mar 2019, 17:26
[GMAT math practice question]

(b-a)/ab = 1/a – 1/b. What is the value of 1/2 + 1/6 + 1/12 + … + 1/90?

A. 4/5
B. 5/6
C. 8/9
D. 9/10
E. 11/12

=>

1/2 + 1/6 + 1/12 + … + 1/90
= 1/(1*2) + 1/(2*3) + 1/(3*4) + … + 1(9*10)
= (2-1)/(1*2) + (3-2)/(2*3) + (4-3)/(3*4) + … + (10-9)/(9*10)
= (1/1 – 1/2) + (1/2 – 1/3) + (1/3-1/4) + … + (1/9 – 1/10)
= 1/1 – 1/10
= 9/10

Therefore, D is the answer.
Answer: D
_________________
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 $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 07 Mar 2019, 17:25
[GMAT math practice question]

How many whole numbers between 100 and 400, inclusive, contain the digit 2?

A. 100
B. 125
C. 138
D. 145
E. 150

=>

There are 19 such numbers with hundreds digit 1: 102, 112, 120, 121, …, 129, 132, 142, …, 192.
There are 100 such numbers with hundreds digit 2: 200, 201, 202, 203, …, 299.
There are 19 such numbers with hundreds digit 3: 302, 312, 320, 321, …, 329, 332, 342, …, 392.

Thus, there are a total of 19 + 100 + 19 = 138 such numbers.

Therefore, the answer is C.
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.
"Only $79 for 1 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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

Show Tags

New post 10 Mar 2019, 17:23
[GMAT math practice question]


When 32 is divided by k, the remainder is k-3. What is the value of k?

1) k>20
2) k<40

=>

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 says that 32 = k*q + ( k – 3 ) or 35 = k*q + k = k(q+1).
That is, k is a factor of 35.
So, k = 1, 5, 7 or 35.

Since condition 1) “k>20” yields the unique solution “k=35”, condition 1) is sufficient.

Condition 2) yields k = 1, 5, 7 or 35. Since it does not yield 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 $79 for 1 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]   [#permalink] 10 Mar 2019, 17:23

Go to page   Previous    1  ...  35   36   37   38   39   40   41  ...  52    Next  [ 1032 posts ] 

The Ultimate Q51 Guide [Expert Level]

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderator: DisciplinedPrep






Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne