Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted.
Author 
Message 
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
04 Nov 2018, 20:30
[ Math Revolution GMAT math practice question] If m and n are integers, is m+m2n an even number? 1) m is an even number 2) n is an even 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. m+m2n = m(m+1) – n. Now, m(m+1) is an even number since m(m+1) is the product of two consecutive integers. Thus, the parity of m+m2n depends on the parity of n only. Thus, condition 2) is sufficient. Therefore, B is the answer. Answer: B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
06 Nov 2018, 01:50
[ Math Revolution GMAT math practice question] If the average (arithmetic mean) of p, q, and r is 6, what is the value of r? 1) p=r 2) p=q => 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 asks for the value of r, where r = 18 – ( p + q ). If we know the value of p + q, then we can determine the value or r. Condition 2) implies that p + q = 0. Therefore, r = 0 + r = ( p + q ) + r = 18, and condition 2) is sufficient. Condition 1) If p = 1, q =18, and r = 1, then p + q + r = 18 and r = 1. If p = 2, q =18, and r = 2, then p + q + r = 18 and r = 2. Since it doesn’t give a unique value of r, condition 1) is not sufficient. Therefore, B is the answer. Answer: B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
06 Nov 2018, 21:32
[ Math Revolution GMAT math practice question] m and n are two different numbers selected from the integers between 11 and 20, inclusive. What is the maximum value of mn / (mn)? A. 320 B. 340 C. 360 D. 380 E. 400 => To obtain the maximum value for mn/(mn), mn must be the smallest possible positive number and mn must be the largest possible product. mn is largest when both m and n are largest, that is, when m = 20 and n – 19. In this case, m – n = 1 is as small as possible and mn = 20*19 = 380 is as large as possible. Thus, the maximum value of mn/(mn) is 20*19/(2019) = 380/1 = 380. Therefore, D is the answer. Answer: D
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
08 Nov 2018, 01:47
[ 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
08 Nov 2018, 20:11
[ Math Revolution GMAT math practice question] The fourdigit 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 onedigit 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 29 Apr 2017
Posts: 29
Location: India
Concentration: Finance, Accounting

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
09 Nov 2018, 03:44
Thanks ..its a really informative thread



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
11 Nov 2018, 23:09
[ 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^2xy > 0 => x(xy) > 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
12 Nov 2018, 20:27
[ 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
13 Nov 2018, 18:42
[ 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
14 Nov 2018, 20:22
[ 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
16 Nov 2018, 03:04
[ 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Manager
Joined: 06 Sep 2018
Posts: 72
Location: India
Concentration: Finance, Entrepreneurship
GPA: 4
WE: Analyst (Investment Banking)

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
16 Nov 2018, 04:06
MathRevolution wrote: [ 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.
_________________
The importance of mindset on the GMAT  640 to 690 to 740 (Q49 V42) : https://bit.ly/2R1WaK5



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
18 Nov 2018, 18:18
[ 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
19 Nov 2018, 18:18
[ 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
20 Nov 2018, 18:15
[ Math Revolution GMAT math practice question] Is the 5digit positive integer abc000 divisible by 24? 1) The 3digit integer abc is divisible by 8. 2) The 3digit 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
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
21 Nov 2018, 18:12
[ 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) a2a = 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(a1) = 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
22 Nov 2018, 18:35
[ Math Revolution GMAT math practice question] If xy≠0 and x^2+4y^2=4xy, (x+y)/(xy)=? A. 1 B. √2 C. √3 D. 2 E. 3 => x^2+4y^2=4xy => x^24xy+4y^2=0 => (x2y)^2=0 => x=2y Thus, (x+y)/(xy) = (2y+y)/(2yy) = 3y/y = 3. Therefore, E is the answer. Answer: E
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
25 Nov 2018, 18:39
[ 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
26 Nov 2018, 18:41
[ 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 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: 7758
GPA: 3.82

Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
Show Tags
27 Nov 2018, 18:10
[ Math Revolution GMAT math practice question] Is x^34x>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^34x>0 => x(x^24)>0 => x(x+2)(x2)>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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly 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 Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"




Re: The Ultimate Q51 Guide [Expert Level]
[#permalink]
27 Nov 2018, 18:10



Go to page
Previous
1 ... 29 30 31 32 33 34 35 ... 42
Next
[ 834 posts ]



