GMAT Club Forumhttps://gmatclub.com:443/forum/ Overview of GMAT Math Question Types and Patterns on the GMAThttps://gmatclub.com/forum/overview-of-gmat-math-question-types-and-patterns-on-the-gmat-211809-200.html Page 11 of 41

 Author: MathRevolution [ 13 Nov 2017, 17:37 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question]What is the remainder of x^2 + y^2, when it is divided by 4?1) x and y are different prime numbers.2) x – y = 2=>Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.Since we have 2 variables and 0 equation, C is most likely to be the answer.Conditions 1) & 2)Since x and y are different prime numbers and x – y = 2, both x and y are odd integers. x = 2a + 1 and y = 2b + 1 for some integers a and b. x^2 + y^2 = (2a+1)^2 + (2b+1)^2 = 4a^2 + 4a + 1 + 4b^2 + 4b + 1 = 4(a^2 + a + b^2 + b ) + 2.Thus, its remainder is 2, when it is divided by 4.Both condition 1) and 2) are sufficient.The answer is C.Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.Answer: C

 Author: MathRevolution [ 15 Nov 2017, 17:05 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question]What of the followings is the range of X = 1 + (1/2^2) + (1/3^2) + ...... + (1/100^2),A. 0 < X < 1 B. 1 < X < 2C. 2 < X < 3D. 3 < X < 4E. 4 < X < 5=>1/A^2 < 1/{(A-1}A} = 1/(A-1) – 1/AIt is clear that 1 + (1/2^2) + (1/3^2) + ...... + (1/100^2) > 1.1 + (1/2^2) + (1/3^2) + ...... + (1/100^2) < 1 + 1/(1∙2) + 1/(2∙3) +1/(3∙4) + … + 1/(99∙100) = 1 + ( 1/1 – 1/2 ) + ( 1/2 – 1/3 ) + … + (1/99 – 1/100)= 1 + 1/1 – 1/100 = 2 – 1/100 < 2Thus 1 < X < 2.Therefore, B is the answer. Answer: B

 Author: MathRevolution [ 28 Nov 2017, 17:04 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question] If 0<2x+3y<50 and -50<3x+2y<0, then which of the following must be true?I. x>0 II. y>0 III. xWhen we add the two inequalities 0<2x+3y<50 and -50<3x+2y<0, we obtain -50<5x+5y<50, or -20<-2x-2y< 20.Statement I. Adding the two inequalities -50<3x+2y<0 and -20<-2x-2y< 20 yields -70

 Author: MathRevolution [ 30 Nov 2017, 00:34 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question]i, j, and k are non-negative integers such that i+j+k=3. If p, q, and r are three fixed, but different, prime numbers, how many different values of p^iq^jr^k are possible? A. 8 B. 9 C. 10 D. 11 E. 12=>The number of possible values of p^iq^jr^k is equal to the number of solutions of the equation i + j + k = 3.The solution set of the equation i + j + k = 3 includes all permutations of (3,0,0), (2,1,0), and (1,1,1).The number of permutations of (3,0,0) is 3!/2! = 3.The number of permutations of (2,1,0) is 3! = 6.The number of permutations of (1,1,1) is 1.Therefore, the number of solutions of the equation i+j+k=3 is 3 + 6 + 1 = 10.Therefore, the answer is C.Answer: C

 Author: MathRevolution [ 03 Dec 2017, 17:45 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question]Nov. 18th fell on a Thursday in 1999. On which day did Nov. 18th fall in 2005? A. Tuesday B. Wednesday C. Thursday D. Friday E. Saturday=>If a year is divisible by 400, it is a leap year.If a year is divisible by 100, but not divisible by 400, it is not a leap year.If a year is divisible by 4, but not divisible by 100, it is a leap year.The day on which a particular date falls will be shifted by two days from one year to the next if the next year is a leap year, and by one day from one year to the next if the next year is not a leap year. For example, Nov. 18th fell on a Thursday in 1999, and a Saturday in 2000 since 2000 was a leap year. It fell on a Saturday in 2000, and a Sunday in 2001 since 2001 was not a leap year.As there were two leap years (2000 and 2004) between 1999 and 2005, Nov. 18th shifted by 8 days over the 6-year period. If a date is shifted by 7 days, it will fall on the same day of the week. So, the net effect was to shift Nov. 18th by one day. Therefore, Nov 18th fell on a Friday in 2005, and the answer is D. Answer: D

 Author: MathRevolution [ 07 Dec 2017, 17:59 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question]Which of the following is the closest to 11^59^5 – 2(10^5)?A. 10^2 B. 10^7 C. 10^8 D. 10^9 E. 10^{10}=>11^59^5 – 2(10^5)≒ 10^510^5 – 2(10^5)= 10^{10} – 2(10^5)≒ 10^{10}Therefore, the answer is E.Answer: E

 Author: MathRevolution [ 17 Dec 2017, 23:34 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question]If x^3y^4z^5<0, is xyz>0? 1) y<02) x<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, and then recheck the question Modifying the original condition gives:x^3y^4z^5<0⇔ xz<0because the signs of an integer and its odd powers are the same. Under the condition xz<0, the question, xyz > 0, is equivalent to asking if y<0.This is exactly condition 1).Therefore, the answer is A.Answer: A

 Author: MathRevolution [ 25 Dec 2017, 17:11 ] Post subject: Re: Overview of GMAT Math Question Types and Patterns on the GMAT [GMAT math practice question]46, 47, 48, 49, 50, 51, 52, 53, 54 The standard deviation of the 9 numbers in the above list lies between 2 and 3. How many of the 9 numbers are within one standard deviation of the average (arithmetic mean)? A. 5 B. 6 C. 7 D. 8 E. 9=>The average of the 9 numbers is 50. So, if n lies within one standard deviation of the mean, then 50 – 2.xxx < n < 50 + 2.xxx47.xxx < n < 52.xxxand n = 48, 49, 50, 51, or 52. There are five numbers in this range.Therefore, the answer is A.Answer : A