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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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27 Jan 2020, 06:06
[GMAT math practice question] (Probability) Among integers from 1 to 50, inclusively, what is the number of the multiples of 4 or 5? A. 14 B. 16 C. 18 D. 20 E. 22 => The number of multiples of 4 is 12 = (48 – 4)/4 + 1 = 11 + 1, since 4, 8, …, 48 are the multiples of 4 between 1 and 50, inclusive. The number of multiples of 5 is 10 = (50 – 5)/5 + 1 = 9 + 1, since 5, 10, …, 50 are the multiples of 5 between 1 and 50, inclusive. Multiples of 20 are doublecounted, and the number of multiples of 20 is 2 since 20 and 40 are multiples of 20 between 1 and 50, inclusive. Then we have 12 + 10  2 = 20. Therefore, D is the answer. Answer: D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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28 Jan 2020, 17:48
[GMAT math practice question] (Geometry) In the figure below, is triangle AEF an isosceles triangle? 1) AB = AC 2) DF is perpendicular to BC. Attachment:
1.22ds.png [ 8.57 KiB  Viewed 215 times ]
=> 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. Visit https://www.mathrevolution.com/gmat/lesson for details. Since triangle AEF has three sides, we have 3 variables (AE, AF, and EF) and 0 equations, and E is most likely 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) We have ∠B = ∠C since AB = AC, and the triangle is isosceles. Assume ∠B = ∠C = x. Then ∠DEC = ∠AEF = 90 – x since the triangle is a right triangle, and ∠DEC is congruent to ∠AEF. Since triangle BDF is a right triangle, we have ∠AFE = 90 – x. Thus we have ∠AEF = ∠AFE, which means the triangle is isosceles, and we have AE = AF. Since both conditions together yield a unique solution, they are sufficient. 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.
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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02 Feb 2020, 18:33
[GMAT math practice question] (Geometry) What is the measure of ∠BIC in the figure? 1) Point I is the incenter (the point where the three angle bisectors meet) of triangle ABC. 2) ∠BAC = 50° Attachment:
1.28ds.png [ 4.2 KiB  Viewed 192 times ]
=> 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. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 4 variables (∠BIC, ∠ABC, ∠BCA, and ∠CAB) and 1 equation (∠ABC + ∠BCA + ∠CAB = 180°), C is most likely 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 point O is the incenter of triangle ABC from condition 1), the segments IA, IB, and IC are bisectors of ∠BAC, ∠ABC and ∠BCA, respectively. ∠BIC = 180° – (∠IBC + ∠ICB), ∠BIC = 180° – (1/2)(180°  ∠BAC), ∠BIC = 180° – (1/2)(180°  50°), ∠BIC = 180° – 65° = 115°. Since both conditions together yield a unique solution, they are sufficient. 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 in which the answer is A, B, C, or D.
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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: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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05 Feb 2020, 17:21
[GMAT math practice question] (Number Properties) If 100! = 100 x 99 x…x 2 x 1 can be written as 2^a3^b5^c7^d…., what is a? A. 86 B. 97 C. 108 D. 119 E. 131 => We need to count the number of prime factors 2 in the prime factorization of 100!. We can do it by counting: The number of multiples of 2 is [100/2] = 50. The number of multiples of 4 is [100/4] = 25. The number of multiples of 8 is [100/8] = 12. The number of multiples of 16 is [100/16] = 6. The number of multiples of 32 is [100/32] = 3. The number of multiples of 64 is [100/64] = 1. Thus the number of prime factors 2 is 50 + 25 + 12 + 6 + 3 + 1 = 97. Therefore, the answer is B. Answer: B
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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09 Feb 2020, 17:29
[GMAT math practice question] (Geometry) The figure below shows the dimensions of triangle ABC. What is ∠BIC? 1) Point I is the incenter of △ABC. 2) Line DE is parallel to line BC. Attachment:
2.4DS.png [ 8.92 KiB  Viewed 134 times ]
=> 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. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Condition 1) Since we can find an incenter of a triangle by the intersection of lines bisecting interior angles, ∠DBI is equal to ∠IBC, and ∠ECI is equal to ∠ICB. Attachment:
2.4DS(A).png [ 10.96 KiB  Viewed 134 times ]
Then we have ∠IBC = 22° and ∠ICB = 30°. Thus, we have ∠BIC = 180°  ∠IBC  ∠ICB = 180° – 22° – 30° = 128°. Since condition 1) yields a unique solution, it is sufficient. Condition 2) Since we don’t know the position of I on segment DE, condition 2) does not yield a unique solution, and it is not sufficient. Therefore, A is the answer. Answer: A
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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: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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11 Feb 2020, 18:11
[GMAT math practice question] (Algebra) What is the value of [x] + [x]? ([x] means the greatest integer less than or equal to x.) 1) 0 ≤ x. 2) x is not 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. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. If x = n + h where n is an integer and 0 ≤ h < 1, then [x] = n. Here n is the integer part of n, and h is the decimal part of n. If x is an integer, then we have x = n + h where h = 0, [x] = n, [x] = n and [x] + [x] = n + (n) = 0. Assume x is not an integer. Then we have x = n + h where 0 < h < 1, [x] = n. We have x = n  h, x = n  1 + 1  h, x = (n + 1) + (1  h) where 0 < 1  h < 1. Thus [x] = n  1 and we have [x] + [x] = n + (n  1) = 1. Condition 2) tells us that x is not an integer. Therefore [x] + [x] = 1 and condition 2) yields a unique solution. Condition 2) is sufficient. Condition 1) If x = 0 which is an integer, then we have [x] + [x] = 0. If x = 1.5 which is not an integer, then we have [x] + [x] = 1. Since condition 1) does not yield a unique solution, it is not sufficient. Therefore, B is the answer. Answer: B
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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: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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13 Feb 2020, 18:26
[GMAT math practice question] (Geometry) In the figure below, point I is the incenter of △ABC and line AH is perpendicular to BC. If ∠ABC = 80 and ∠ACB = 50 what is ∠x + ∠y? Attachment:
2.4PS.png [ 17.52 KiB  Viewed 100 times ]
A. 55 B. 60 C. 65 D. 75 E. 80 => ∠BAC = 180 – 80 – 50 = 50. An incenter of a triangle is the intersection of lines bisecting all interior angles. ∠x = ∠CAH  ∠CAI = 40 – 25 = 15. ∠y = ∠CAI + ∠ACI = 25 + 25 = 50. Thus ∠x + ∠y = 15 + 50 = 65. Therefore, C is the answer. Answer: C
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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: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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16 Feb 2020, 17:59
[GMAT math practice question] (Geometry) The figure shows parallelogram ABCD and point E on line AD. What is the ratio of △ABE : △DCE? 1) The area of ABCD is 50. 2) AE : ED = 3 : 2. Attachment:
2.11DS.png [ 15.24 KiB  Viewed 92 times ]
=> 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. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Since triangles ABE and DCE have the same height, we have △ABE : △DCE = AE : ED. Thus, condition 2) is sufficient. Condition 1) Since we don’t know AE : ED, condition 1) is not sufficient. Therefore, B is the answer. Answer: B
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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: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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18 Feb 2020, 17:41
[GMAT math practice question] (Number Properties) For positive integers A and B, G is the greatest common divisor of A and B, and L is the least common multiple of A and B. What is A + B? 1) L = 70 2) G/A + G/B = 7/10 => 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. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 2 variables (A and B) and 0 equations, C is most likely 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) Assume A = aG and B = bG where a and b are relatively prime numbers. Since G/A + G/B = 7/10 from condition 2), we have G/A + G/B = 7/10, G/aG + G/bG = 7/10 (substituting in A = aG and B = bG), bG/abG + aG/abG = 7/10 (getting a common denominator), (aG + bG)/abG = 7/10 (adding the fractions), (A + B)/L = 7/10 (substituting A = Ag, B = bG, and L = abG). Since L = 70 from condition 1), we have (A + B)/L = 7/10, (A + B)/70 = 7/10 or A + B = 49. Since both conditions together yield a unique solution, they are sufficient. Since this question is a statistics 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 = 70 and B = 1, then we have A + B = 71. If A = 70 and B = 2, then we have A + B = 72. Since condition 1) does not yield a unique solution, it is not sufficient. Condition 2) Assume A = aG and B = bG where a and b are relatively prime numbers. G/A + G/B = 1/a + 1/b = 7/10. If a = 2, b = 5, and G = 1, then we have A = aG = 2(1) = 2, B = bG = 5(1) = 5 and A + B = 2 + 5 = 7. If a = 2, b = 5, and G = 2, then we have A = aG = 2(2) = 4, B = bG = 5(2) = 10 and A + B = 4 + 10 = 14. Since condition 2) does not yield a unique solution, it is not sufficient. 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.
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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19 Feb 2020, 17:56
[GMAT math practice question] (Geometry) The figure below shows parallelogram ABCD, where line DH is perpendicular to line BC. P is a point inside parallelogram ABCD. If AD = 7, DH = 4 and the area of triangle PBC is 5, what is the area of triangle PAD? Attachment:
2.11PS.png [ 7.03 KiB  Viewed 49 times ]
A. 8 B. 9 C. 10 D. 11 E. 12
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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: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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20 Feb 2020, 17:42
[GMAT math practice question] (Geometry) The figure below shows parallelogram ABCD and point E is on line BC. Line DE bisects ∠D. Moreover, BE = DE and ∠A = 120°. What is the measure of ∠BDE? A. 20° B. 30° C. 33° D. 40° E. 43° Attachment:
2.13PS.png [ 9.96 KiB  Viewed 38 times ]
=> Since BE = DE, we have ∠DBE = ∠BDE and ∠DEC = 2*(∠BDE) = 2*(∠EDC). Since ∠EDC + ∠DEC + ∠C = 180°, ∠EDC + 2*(∠EDC) + 120° = 180°, 3*(∠EDC) + 120° = 180°, 3*(∠EDC) = 60°, ∠EDC = 20°. Then we have ∠BDE = ∠EDC = 20°. Therefore, the answer is A. Answer: A
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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: 8591
GPA: 3.82

Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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23 Feb 2020, 18:20
[GMAT math practice question] (Equation) What is the value of abc? 1) a + 4/b = 1 2) b + 1/c = 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. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Since we have 3 variables (a, b, and c) and 0 equations, E is most likely 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. The question  is equivalent to  for the following reason Conditions 1) & 2) When we multiply both sides of the equation a + 4/b = 1 by b, we have ab + 4 = b. When we multiply both sides of the equation b + 1/c = 4 by c, we have bc + 1 = 4c or bc = 4c – 1. When we multiply both sides of the equation ab + 4 = b by c, we have abc + 4c = bc. When we replace bc of the equation abc + 4c = bc by 4c – 1, we have abc + 4c = 4c – 1 or abc = 1. Since both conditions together yield a unique solution, they are sufficient. 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 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 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: Overview of GMAT Math Question Types and Patterns on the GMAT
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