Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
09 Nov 2016, 01:36
(ex 20) (function) In(on) the xy coordinate plane, what is the area of a circle K? 1) The circle has (2,1) as its center 2) The circle passes through a point (3,4) ==>In the original condition, since the circle is on the coordinate plane, there are 3 variables (the center (a,b)) and becomes the radius r), so E is highly likely to be the answer. Through 1) & 2), you get the radius r=√(〖(23)〗^2+〖(14)〗^2 )=√(1+9)=√10, and the area of the circle is π(√10)^2=10π. Since the answer is unique, it is sufficient. The answer is C. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
10 Nov 2016, 01:18
There is an arithmetic sequence An where n is a positive integer such that An+1=An+3, what is the value of A10? 1) A1=3. 2) A3+A6=27 ==>In the original condition, there are 2 variables (An+1, An), and 1 equation (An+1=An+3), so D is highly likely to be the answer. 1)=2), so you get A10=30, hence unique, and sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
11 Nov 2016, 01:06
If x/300=y/100, x=? 1) x+y=400 2) y=100 ==>In the original condition, there are 2 variables (x,y) and 1 equation (x/300=y/100), so D is highly likely to be the answer. Hence 1)=2), the remainder of both is x=300, so it is unique, and sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
14 Nov 2016, 01:32
Is x1>x3? 1) x>2 2) x>1 ==>If you modify the original condition and the problem, the sign of inequality does not change even if you square both sides. In other words, x1>x3?,Is x1^2>x3^2?, (x1)^2>(x3)^2?, and if you expand this, you get x^22x+1>x26x+9?, 6x2x>91?, 4x>8?. That is, you get x>2?. 1) is yes, and sufficient. 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"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
14 Nov 2016, 01:33
For all integers k, the function g is defined by g(k) = ak+4, where a is a constant. What is the value of g(1)? (1) g(3) = 7 (2) g(1) =3 If you modify the original condition and the problem, you get g(1)=a×1+4=a+4=?. Since you get 1 variable(a), and in order for it to match with the number of equation it needs one, hence 1 for 1), and 1 for 2). Thus, there is high chance that D is the answer. In the case of 1), from g(3)=3a+4=7 you get a=1, therefore unique and sufficient. In the case of 2), from g(1)=a(1)+5=a+4=3 you get a=1, therefore unique and sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
17 Nov 2016, 04:16
m=? 1) 3^ 3m1=9 2) 5^ 2m+1=125 ==> In the original condition, there is 1 variable (m), and therefore D is most likely to be the answer. In case of con 1), from 3^ 3m1=9=3^2, you get 3m1=2 and m=1, and hence it is sufficient. In case of con 2), from 5^ 2m+1=125=5^3 and 2m+1=3, you get m=1, and hence it is sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
18 Nov 2016, 01:23
If x and y are integers greater than 1 and x>y, what are the values of x and y? 1) x+y=14 2) xy=33 ==> In the original condition, there are 2 variables (x, y) and therefore C is most likely to be the answer. By solving con 1) and con 2), you get x=11 and y=3. However, since this question is an integer question, one of the key questions, if you apply CMT 4 (A), in case of con 1), from x=11, y=3 or x=10 y=4, it is not unique and not sufficient, and in case of con 2), you only get x=11 and y=3, and hence it is unique and sufficient. 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"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Math Revolution Approach (DS)
[#permalink]
Show Tags
Updated on: 22 Nov 2016, 00:39
Is ab+cd>0? 1) ac+db>0 2) ad+bc>0 ==> In the original condition, there are 4 variables (a, b, c, d). Therefore, E is most likely to be the answer. By solving con 1) and con 2), (a, b, c, d) = (3, 4, 1, 1) is no, and (1,1,1,1) is yes. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
21 Nov 2016, 02:01
What is the standard deviation of 3 products’ prices? 1) The sum of any two prices of these 3 products is $1,000 2) At least one of them is 500 ==> In the original condition, there are 3 variables. Therefore, E is most likely to be the answer. For con 1), the sum of any 2 prices of the products is always 1,000, so if you add the three equations a+b=1,000, b+c=1,000, and c+a=1,000 together, you get 2(a+b+c)=3,000 and a+b+c=1,500 each, and using substitution, a=b=c=500. Thus, the standard deviation is 0, hence it is sufficient. Therefore, the answer is A. This question is CMT 4 (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"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
23 Nov 2016, 01:19
If x is positive integer, is √2x an integer? 1) x/2 is an integer squared 2) x/200 is an integer squared ==> In the original condition, there is 1 variable (x). Therefore, D is most likely to be the answer. For con 1), from x=2t^2, you get √2x = √(2*2t^2 ) =2t, hence yes, it is sufficient. For con 2), from x=200s^2, you get √2x = √(2*200s^2 ) =20s, hence yes, it is sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
24 Nov 2016, 02:41
If a+b is even, is b an integer? 1) ab=integer 2) a+3b=even ==> In the original condition, there are 2 variables (a, b) and 1 equation (a+b=even). Therefore, D is most likely to be the answer. For con 1), a=b=1 is yes, and a=5/2, b=1/2 is no, hence it is not sufficient. For con 2), a+3b=a+b+2b=even, even+2b=even, 2b=even, b=integer, hence yes, it is sufficient. Therefore, the answer is B. This type of question is a 5051level question related to CMT 4 (A). 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
25 Nov 2016, 02:20
The question below is also a 5051level question, a typical integer question. When a positive integer n has 6 different factors, n=? 1) n has 2 prime factors 2) n<18 ==> In the original condition, in case of standard deviation questions, there is 1(n) variable, and therefore D is most likely to become the answer. In case of con 1), you get \(n=2^23^1, 2^13^2,\) hence it is not unique and not sufficient. In case of con 2), you get only \(n=2^23^1\), hence it is unique and sufficient. 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"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
28 Nov 2016, 01:34
Is x<0? 1) \(x^5\)<0 2)\(x^5\)+x+1=0 ==> In the original condition, there is 1 variable, and therefore D is most likely to be the answer. In case of con 1), from \(x^5\)<0, if you divide both sides by \(x^4\), you get x<0, hence yes, it is sufficient. In case of con 2), it cannot be factored, and this is when you use CMT 4 (B). In other words, if you get A and B too easily, then consider D. Since\(x^5\)+x=1, x(\(x^4\)+1)=1, and x=1/\((x^4\)+1) always agree with x4+1>0, and hence yes, it is sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
28 Nov 2016, 01:36
If \(a^3b^4c^5<0\), is abc<0? 1) c<0 2) b>0 ==> If you modify the original condition and the question, when you divide both sides of \(a^3b^4c^5<0\) by \(a^2b^4c^4,\) you get ac<0, and the question abc<0? becomes b>0?. From con 2) b>0, it becomes yes, hence it is sufficient. 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"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
30 Nov 2016, 03:08
If m and n are positive integers, is \(n^mn\) divisible by 6? 1) m=3 2) n=2 ==> In the original condition, there are 2 variables (m,n), and in order to match the number of variables to the number of equations, there must be 2 equations. Therefore, C is most likely to be the answer. By solving con 1) and con 2), from\(2^32=6\), you get yes, and hence it is sufficient. The answer is C. However, this question is an integer question, one of the key questions, so you need to apply CMT 4. For con 1), from \(n^3n=(n1)n(n+1)\), it is the multiple of the three consecutive integers, which always becomes the multiple of 6, hence yes, it is sufficient. For con 2), from n=2 and m=3 yes, m=2 no, and hence it is not sufficient. 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"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
01 Dec 2016, 01:57
ab=ba? 1) a<b 2) ab<0 and \(a^2b\)=1 ==> If you modify the original condition and question, to get A=A, you need to get A≤0?, so it becomes ab=ba=(ab)?, ab<0?, a<b?. Thus, for con 1), it is always yes, hence sufficient, and for con 2), if you apply CMT 4 (B), it also becomes a<b, hence yes, it is sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
02 Dec 2016, 01:32
If x is a positive integer greater than 1, is 1/x a terminating decimal? 1) x has 3 as a factor 2) x is a factor of 81 ==> If you modify the original condition and the question, to get 1/x as the terminating decimal, only 2 or 5 can be the prime factors of denominator x. However, for con 2), in order for x to become factors of 81=\(3^4\), only 3 can be the prime factor of x, hence no, it is sufficient. 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"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
05 Dec 2016, 01:34
If 5 different positive integers have 3 as its median, is the average (arithmetic mean) of them greater than 5? 1) The greatest integer of them is 16 2) The smallest integer of them is 1 ==> If you modify the original condition and the question, the sum of 5 integers>585=25?, and so there are 5 variables and 1 equation. Therefore, E is most likely to be the answer. However, if the question is “greater than”, you need to find the least value. By solving con 1) and con 2), The least value of the sum becomes 1+2+3+4+16=26>25 yes, hence it is sufficient. The answer is C. However, this question is a key question, so you need to apply CMT 4 (A). For con 1), the least value of the sum=1+2+3+4+16=26>25, hence yes, it is sufficient. For con 2), 1+2+3+4+5=15<25 is no, 1+2+3+10+30=46>25 is yes, hence it is not sufficient. Therefore, the answer is A. This question, related to CMT 4 (A), is 5051level question in current GMAT. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
05 Dec 2016, 01:37
x=? 1) 1.1x=1.2x 2) \(1.1x^2\)=\(1.2x^2\) ==> In the original condition, there is 1 variable (x), and in order to match the number of variables to the number of equations, there must be 1 equation as well. Therefore, D is most likely to be the answer. For con 1), you get from 2.3x=0 to x=0, hence it is unique and sufficient, and For con 2), you get from 2.3x2=0 to x=0, hence it is also unique and sufficient. 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: 8003
GPA: 3.82

Re: Math Revolution Approach (DS)
[#permalink]
Show Tags
07 Dec 2016, 01:33
What is the median of the 9 numbers? 1) The smallest 5 numbers of them are less than or equal to 10. 2) The largest 5 numbers of them are more than or equal to 10. ==> In the original condition, since there are 9 variables, E is likely to be the answer. Through 1) & 2), in order of size, the first 5 numbers are smaller than 10 or the same. Also, the last 5 numbers are bigger than 10 or the same. Hence, the fifth number should be always 10. Then, the fifth number becomes median and median=10, which is unique and sufficient. Hence, the answer is 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"




Re: Math Revolution Approach (DS)
[#permalink]
07 Dec 2016, 01:33



Go to page
Previous
1 2 3 4 5 6 7 8 9 10 11 ... 29
Next
[ 573 posts ]



