GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Apr 2019, 07:48

### 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

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

# Math Revolution DS Expert - Ask Me Anything about GMAT DS

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

31 Mar 2019, 18:37
MathRevolution wrote:
[GMAT math practice question]

The diagram below contains four right triangles with legs a and b. What is the area of the larger square?

Attachment:
3.29.png

1) a = 12
2) b = 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.

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

If we assume $$c$$ is the length of the hypotenuse of the right triangle, we have $$c^2 = a^2 + b^2$$ and $$c^2$$ is the area the larger square.
We need the values of both $$a$$ and $$b$$. Thus, conditions 1) & 2) are sufficient, when applied together, but neither condition is sufficient on its own.

_________________
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 $149 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 Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 01 Apr 2019, 02:52 [GMAT math practice question] (absolute value) Is $$x<y<z$$ ? $$1) |x+1|<y<z+1$$ $$2) |x-1|<y<z-1$$ _________________ 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$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Director
Joined: 23 Feb 2015
Posts: 857
GMAT 1: 720 Q49 V40

### Show Tags

01 Apr 2019, 16:26
MathRevolution wrote:
[GMAT math practice question]

(number properties) 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

fskilnik,
Sir, is it possible to solve this question by rotations style?
Thanks__
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

01 Apr 2019, 21:12
Sandeepanisha wrote:
(integer) [x] is the greatest integer less than or equal to x, is x-[x]>0?

1) x is positive
2) x is not integer

[x] is the integer part of x.
If x = n + h where n is an integer and 0 ≤ h < 1, then [x] = n.
For example, if x = 1.2 = 1+0.2, then [x] = 1.

Thus x - [x] = n + h - n = h is the decimal part of x.
x - [x] > 0 means h > 0 and x is not an integer.
Thus condition 2) is sufficient.

Condition 1)
If x = 1.2, then x - [x] = 1.2 - 1 = 0.2 > 0 and the answer is 'yes'.
If x = 1, then x - [x] = 1 - 1 = 0 and answer is 'no'.
Since we don't have a unique answer, condition 1) is not sufficient.

_________________
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 $149 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 Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 01 Apr 2019, 21:19 1 Sandeepanisha wrote: (ratio) All of the households used a total of x watts for 24 hours and one household used y watts per hour. What is the total number of all the households, in terms of x and y? A. x/y B. 24x/y C. x/24y D. 24xy E. 24/xy Let n be the number of households. Then we have 24y*n = x, which is the total waats they use. Thus n = x/(24y). Therefore, then answer is 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$149 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
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

02 Apr 2019, 07:49
[GMAT math practice question]

(absolute values) If $$|2x|>|3y|$$, is $$x >y$$?

$$1) x>0$$
$$2) y>0$$
_________________
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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 932 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 02 Apr 2019, 13:19 AsadAbu wrote: MathRevolution wrote: [GMAT math practice question] (number properties) 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 fskilnik, Sir, is it possible to solve this question by rotations style? Thanks__ Hi, AsadAbu . Thank you for your interest in my opinions, but (by contract) I must limit myself to post questions/solutions (and some brief explanations about our solutions, when asked). I am not here to judge or compare GMATH´s method to other experts/companies approaches. Thank you for your understanding. Regards and success in your studies, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Director Joined: 23 Feb 2015 Posts: 857 GMAT 1: 720 Q49 V40 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 02 Apr 2019, 14:10 fskilnik wrote: AsadAbu wrote: MathRevolution wrote: [GMAT math practice question] (number properties) 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 fskilnik, Sir, is it possible to solve this question by rotations style? Thanks__ Hi, AsadAbu . Thank you for your interest in my opinions, but (by contract) I must limit myself to post questions/solutions (and some brief explanations about our solutions, when asked). I am not here to judge or compare GMATH´s method to other experts/companies approaches. Thank you for your understanding. Regards and success in your studies, Fabio. Yep, I get it. Thanks__ _________________ “The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” Henry Wadsworth Longfellow Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 03 Apr 2019, 04:14 MathRevolution wrote: [GMAT math practice question] (absolute value) Is $$x<y<z$$ ? $$1) |x+1|<y<z+1$$ $$2) |x-1|<y<z-1$$ => 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 $$3$$ 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) By condition 1), $$x < y$$ since $$x < x + 1 ≤ | x + 1 | < y$$. By condition 2), $$y < z$$ since $$y < z – 1 < z.$$ Therefore, $$x < y < z$$. Thus, both conditions 1) & 2) together are sufficient. Since this question is an absolute value 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 $$x = 1, y = 3$$, and $$z = 5,$$ then the answer is ‘yes’. If $$x = 1, y = 3,$$ and $$z = 2.9$$, then the answer is ‘no’ since z < y. Thus, condition 1) is not sufficient, since it does not yield a unique solution. Condition 2) If $$x = 1, y = 3,$$ and $$z = 5$$, then the answer is ‘yes’. If $$x = 3.1, y = 3,$$ and $$z = 5$$, then the answer is ‘no’ since $$x > y$$. Thus, condition 2) is not sufficient, since it does not yield a unique solution. Therefore, C is the answer. Answer: C 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$149 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
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

03 Apr 2019, 04:15
[GMAT math practice question]

$$m$$ and $$n$$ are positive integers. Are $$m$$ and $$n$$ consecutive integers?

$$1) m^2+n^2 = 5$$
$$2) m-n = 1$$
_________________
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 $149 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 Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 04 Apr 2019, 00:32 MathRevolution wrote: [GMAT math practice question] (absolute values) If $$|2x|>|3y|$$, is $$x >y$$? $$1) x>0$$ $$2) y>0$$ => 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. From condition 1), we have $$3x > 2x = |2x| > |3y| ≥ 3y$$ since $$|x| = x.$$ So, $$x > y$$ and the answer is ‘yes’. Thus, condition 1) is sufficient. Condition 2) If $$x = 10$$, and $$y = 1$$, then $$x > y$$ and the answer is ‘yes’. If $$x = -10$$, and $$y = 1,$$ then $$x < y$$ and the answer is ‘no’. Thus, 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$149 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
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

04 Apr 2019, 00:33
[GMAT math practice question]

(number properties) $$m$$ and $$n$$ are integers. Is $$m + n$$ an odd number?

$$1) m – n = 2$$
$$2) m^2n^2 = 225$$
_________________
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 $149 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 Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 05 Apr 2019, 01:41 MathRevolution wrote: [GMAT math practice question] $$m$$ and $$n$$ are positive integers. Are $$m$$ and $$n$$ consecutive integers? $$1) m^2+n^2 = 5$$ $$2) m-n = 1$$ => 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. Condition 1) The only positive integers satisfying $$m^2+n^2 = 5$$ are $$m = 1$$ and $$n = 2$$, or $$m=2$$ and $$n = 1.$$ These are consecutive integers, so condition 1) is sufficient. Condition 2) Since the difference between $$m$$ and $$n$$ is $$1$$, they are consecutive integers. Condition 2) is sufficient. 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$149 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
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

05 Apr 2019, 01:41
[GMAT math practice question]

(inequality) Is $$x < 0$$?

$$1) x^3 + 1 < 0$$
$$2) x^3 + x + 1 < 0$$
_________________
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 $149 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 Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 07 Apr 2019, 18:38 MathRevolution wrote: [GMAT math practice question] (number properties) $$m$$ and $$n$$ are integers. Is $$m + n$$ an odd number? $$1) m – n = 2$$ $$2) m^2n^2 = 225$$ => 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) Since $$m^2n^2 = 225$$ is an odd number, both $$m$$ and $$n$$ must be odd numbers, and $$m + n$$ is an even number. Thus, the answer is ‘no’, and condition 2) is sufficient by CMT (Common Mistake Type) 1. Condition 1) Since $$m – n = 2$$, both $$m$$ and $$n$$ are odd numbers or even numbers. Since $$m$$ and $$n$$ have the same parity, $$m + n$$ is an even number. Thus, the answer is ‘no’, and condition 1) is sufficient by CMT (Common Mistake Type) 1. 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$149 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
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

07 Apr 2019, 18:39
MathRevolution wrote:
[GMAT math practice question]

(inequality) Is $$x < 0$$?

$$1) x^3 + 1 < 0$$
$$2) x^3 + x + 1 < 0$$

=>

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.

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)
$$x^3 + 1 < 0$$
$$=> (x+1)(x^2-x+1) < 0$$
$$=> x + 1 < 0$$ since $$x^2-x+1 > 0$$
$$=> x < -1 < 0$$
Thus, condition 1) is sufficient, and the answer is ‘yes’.

Condition 2)
$$x^3 + x + 1 < 0$$
$$=> x^3 + x < -1$$
$$=> x(x^2 + 1) < -1$$
$$=> x < \frac{-1}{(x^2 + 1)}$$ since $$x^2 + 1 > 0$$
$$=> x <\frac{-1}{(x^2 + 1)} < 0$$ since $$x^2 + 1 > 0$$
Thus, condition 2) is sufficient, and the answer is ‘yes’.

_________________
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 $149 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 Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 08 Apr 2019, 02:02 [GMAT math practice question] (statistics) If the median and average (arithmetic mean) of a set of 4 different numbers are both 10, what is the smallest number? 1) The range of the 4 numbers is 10 2) The sum of the smallest and the largest numbers is 20 _________________ 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$149 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
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

09 Apr 2019, 00:10
[GMAT math practice question]

(statistics) $$x, y$$ and $$z$$ are different integers. Is their average equal to their median?

1) Their range is $$11$$.
2) Their median is $$11$$.
_________________
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 $149 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 Joined: 16 Aug 2015 Posts: 7251 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS [#permalink] ### Show Tags 10 Apr 2019, 00:43 MathRevolution wrote: [GMAT math practice question] (statistics) If the median and average (arithmetic mean) of a set of 4 different numbers are both 10, what is the smallest number? 1) The range of the 4 numbers is 10 2) The sum of the smallest and the largest numbers is 20 => 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 $$a, b, c$$ and $$d$$ be the $$4$$ numbers, and suppose $$a < b < c < d.$$ Then $$\frac{( a + b + c + d )}{4} = 10$$ and $$\frac{( b + c )}{2} = 10.$$ Since $$b + c = 20$$ and $$a + b + c + d = 40$$, we must have $$a + d = 20.$$ Condition 1) Since $$d – a = 10$$ by condition 1), we can figure out the values of $$a$$ and $$d$$. Thus, condition 1) is sufficient. Condition 2) $$a + d = 20$$ can be deduced from the original condition as shown above. So, condition 2) provides no additional information. If $$a = 1, b = 9, c = 11$$ and $$d = 19$$, then the smallest number is $$1$$. If $$a = 2, b = 9, c =11$$ and $$d = 18$$, then the smallest number is $$2$$. Condition 2) is not sufficient since it does not yield a unique answer. 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$149 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
Joined: 16 Aug 2015
Posts: 7251
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

10 Apr 2019, 00:44
[GMAT math practice question]

(number properties) If $$m$$ and $$n$$ are positive integers, is $$m^2-n^2$$ divisible by $$4$$?

1) $$m^2+n^2$$ has remainder $$2$$ when it is divided by $$4$$

2) $$m*n$$ is an odd integer
_________________
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 \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS   [#permalink] 10 Apr 2019, 00:44

Go to page   Previous    1  ...  8   9   10   11   12   13   14   15   16   17   18   19    Next  [ 362 posts ]

Display posts from previous: Sort by