GMAT Review Questions and 100% Correct Answers "Alexandra needs to mix cleaning solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Alexandra makes a mistake and mixes in half as much bleach as she ought to have. The total solution consists of 27 mL. How mu ch bleach did Alexandra put into the solution? " ✅3 ml "What is the cube root of w ? (1) The 5th root of w is 64. (2) The 15th root of w is 4." ✅D x^y=y^x, where x is prime and y is even ✅If Y is even, Y^x must be even as well. It must be true then that x^y is also even. If x^y is even, X itself must be even. Since x is both even and prime, it must be true that x=2 since 2 is the only even prime "Eco Wildlife Preserve contains 5x zebras and 2x lions, where x is positive. If the lions kill z zebras, is the new ratio of zebras to lions less than 2 to 1? (1) z>x (2)z=4" ✅"(5x-z)/2x < 2/1 5x-z<4x is z>x?" range of f(x)= (x+sq(3))^4 ✅Range of function can never be negative. Raising anything to an even power will result in a non -negative value if y is an integer, then the least possible value of |23 -5y| ✅2 From the consecutive integers -10 to 10 inclusive, 20 integers are randomly chosen with repetitions allowed. What is the least possible value of the product of the 20 integers? ✅-(10)^20 "If m and n are positive integers, is (√m)^n an integer? (1) (√m) is an integer. (2) (√n) is an integer." ✅A On the planet Flarp, 3 floops equal 5 fleeps, 4 fleeps equal 7 flaaps, and 2 flaaps equal 3 fliips. How many floops are equal to 35 fliips? ✅35 fliips x 2 flaaps/3 fliips x 4 fleeps/7 flaaps x 3 floops/5 fleeps = 8 floops A certain fruit stand sold apples for $0.70 each and bananas for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase? ✅0.7a+0.5b=6.30.7a+0.5b=6.3 --> 7a+5b=637a+5b=63. After some trial and error you'll get that only two integer pairs of (a,b) satisfy this equation: (9,0) and (4,7) as we are told that "a customer purchased both apples and bananas" then the first pair is out and we'll have: a=4a=4 and b=7b=7 --> a+b=11a+b=11. " order to complete a reading assignment on time, Terry planned to read 90 pages per day. However, she read only 75 pages per day at first, leaving 690 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time? (A) 15 (B) 16 (C) 25 (D) 40 (E) 46" ✅B "s= {1,2,5,7,X} If x is a positive integer, is the mean of set S greater than 4? (1) the median of set s is greater than 2 (2) the median of set s is equal to the mean of set S" ✅B If the sum of the last 3 integers in a set of 7 consecutive integers is 258, what is the sum of the first 4 integers? ✅330 Idiom NOT by x BUT by y ✅"Think of it this way for structure - the word ""NOT"" is where the two paths diverge, and each path needs to be directly connected to the ""shared"" entry. So... The goal was scored not by Drogba, but by Donovan. Is correct, because ""the goal was scored ... (stop at ""NOT"" and start after ""BUT"") by Donovan"" is a complete statement. " "Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alon e at its constant rate, to produce 800 nails? (A) x/(x+y) (B) y/(x+y) (C) xy/(x+y) (D) xy/(x -y) (E) xy/(y -x)" ✅"Say x=1 hour and y=2 hours (notice that y must be greater than x, since the time for machine A to do the job, which is y hours, must be more than the time for machines A and B working together to do the same job, which is x hours). In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1. Now, plug x=1 and y=2 in the options to see which one yields 2. Only option E fits. Answer: E. " "A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art? (A) 5,000 - z (B) 5,000 - x - y (C) 5,000 - x + z (D) 5,000 - x - y - z (E) 5,000 - x - y + z" ✅"Easier formula to remember is Group1+ Group2 - Both +Neither = Total (Source: Kaplan) So, solution is x + y - z + Neither = 5000 Neither = 5000 - x - y + z ..Choice E!" If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x? I. 1/2x II. -2/x III. 3/x A. I only B. II only C. I and II D. I and III E. II and III ✅Answer= E "According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t - 5)^2 + 500 for 0 ≤ t ≤ 10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum? a) 5:30 b) 7:00 c) 7:30 d) 8:00 e) 9:00" ✅Answer = B 10 years ago, Sana was half as old as byron. if byron is now 15 years older than sana, how old will sana be in 7 years ✅32 "If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z ? (1) x - y = y - z (2) x^2 - y^2 = z" ✅E "What is the total number of coins that Bert and Claire have? (1) Bert has 50 percent more coins than Claire. (2) The total number of coins that Bert and Claire have is between 21 and 28." ✅C How many of the integers that satisfy the inequality (x+2)(x+3) / (x -2) >= 0 are less than 5? ✅Answer is (D) - 4 "If [x] denotes the least integer greater than or equal to x, is [x] = 0? (1) -1< x< 1 (2) x < 0" ✅C "If x is negative, is x < -3 ? (1) x^2 > 9 (2) x^3 < -9" ✅A "If n and k are positive integers, is sq(n+k) > 2√n (1) k > 3n (2) n + k > 3n" ✅ "Company Q plans to make a new product next year and sell each unit of this new product at a selling price of $2. The variable costs per unit in each production run are estimated to be 40% of the selling price, and the fixed costs for each production run a re estimated to be $5,040. Based on these estimated costs, how many units of the new product will Company Q need to make and sell in order for their revenue to equal their total costs for each production run?
