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09 Dec 2019, 18:37
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[GMAT math practice question]
(absolute value) What is the value of a?
1) |x - 1| = -(ax - 1)^2.
2) |ax - 1| = -√(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.
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)
|x - 1| = -(ax - 1)^2 is equivalent to x = 1 and a = 1 for the following reason.
|x - 1| = -(ax - 1)^2
=> |x - 1| + (ax - 1)^2 = 0
=> x - 1 = 0 and ax - 1 = 0
=> x - 1 = 0 and a - 1 = 0
=> x = 1 and a = 1
Since condition 1) yields a unique solution, it is sufficient.
Condition 2)
|ax - 1| = -√(x - 1) is equivalent to x = 1 and a = 1 for the following reason.
|ax - 1| = -√(x - 1)
=> |ax - 1| + √(x - 1) = 0
=> ax - 1 = 0 and √(x-1) = 0
=> a - 1 = 0 and x - 1 = 0
=> a = 1 and x = 1
Since condition 2) yields a unique solution, it is sufficient.
Therefore, D is the answer.
Answer: D
Note: Tip 1) of the VA method states that D is most likely the answer if condition 1) gives the same information as condition 2).
(absolute value) What is the value of a?
1) |x - 1| = -(ax - 1)^2.
2) |ax - 1| = -√(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.
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)
|x - 1| = -(ax - 1)^2 is equivalent to x = 1 and a = 1 for the following reason.
|x - 1| = -(ax - 1)^2
=> |x - 1| + (ax - 1)^2 = 0
=> x - 1 = 0 and ax - 1 = 0
=> x - 1 = 0 and a - 1 = 0
=> x = 1 and a = 1
Since condition 1) yields a unique solution, it is sufficient.
Condition 2)
|ax - 1| = -√(x - 1) is equivalent to x = 1 and a = 1 for the following reason.
|ax - 1| = -√(x - 1)
=> |ax - 1| + √(x - 1) = 0
=> ax - 1 = 0 and √(x-1) = 0
=> a - 1 = 0 and x - 1 = 0
=> a = 1 and x = 1
Since condition 2) yields a unique solution, it is sufficient.
Therefore, D is the answer.
Answer: D
Note: Tip 1) of the VA method states that D is most likely the answer if condition 1) gives the same information as condition 2).
12 Dec 2019, 18:25
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[GMAT math practice question]
(algebra) A shop hired new employees recently. The number of male employees increased by 10% and the number of female employees decreased by 10%. As a result, the number of all employees increased by 10 individuals, which is a 2% increment. How many male and female employees are there after the recent hiring?
A. 280, 250
B. 300, 200
C. 330, 180
D. 340, 180
E. 350, 200
=>
Assume m and f are the numbers of male and female employees before hiring, respectively.
We have (m + f)*(2/100) = 10 or m + f = 500, since the number of employees increased by 2%.
We have m(10/100) - f(10/100) = 10 or m - f = 100, since the number of male employees increased by 10% and the number of female employees decreased by 10%.
When we add two equations, we have (m + f) + (m - f) = 500 + 100, 2m = 600 or m = 300.
Then f = 500 – m = 200.
There are 1.1m = 330 male employees and 0.9f = 180 female employees.
Therefore, C is the answer.
Answer: C
(algebra) A shop hired new employees recently. The number of male employees increased by 10% and the number of female employees decreased by 10%. As a result, the number of all employees increased by 10 individuals, which is a 2% increment. How many male and female employees are there after the recent hiring?
A. 280, 250
B. 300, 200
C. 330, 180
D. 340, 180
E. 350, 200
=>
Assume m and f are the numbers of male and female employees before hiring, respectively.
We have (m + f)*(2/100) = 10 or m + f = 500, since the number of employees increased by 2%.
We have m(10/100) - f(10/100) = 10 or m - f = 100, since the number of male employees increased by 10% and the number of female employees decreased by 10%.
When we add two equations, we have (m + f) + (m - f) = 500 + 100, 2m = 600 or m = 300.
Then f = 500 – m = 200.
There are 1.1m = 330 male employees and 0.9f = 180 female employees.
Therefore, C is the answer.
Answer: C
15 Dec 2019, 18:29
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[GMAT math practice question]
(geometry) ABCD and AFGE are rectangles, and the area of ABCD is 120. What is the area of the rectangle AFGE?
1) The area of GBC is 24.
2) The area of EGD is 9.
12.11DS.png [ 9.68 KiB | Viewed 2624 times ]
=>
We can draw an additional line GH on the figure.
12.11DS(A).png [ 9.84 KiB | Viewed 2581 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) tells us that the area of rectangle BFHC is 48 since it is two times greater than the area of triangle GBC.
Condition 2) tells us that the area of rectangle EGHD is 18 since it is two times greater than the area of triangle EGD.
Then we have AFGE = ABCD – (FBCH + EGHD).
Since we have 4 variables (AFGE, ABCD, FBCH and EGHD) and 2 equations (ABCD = 120 and AFGE = ABCD – (FBCH + EGHD)), 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)
AFGE = ABCD – (FBCH + EGHD) = 120 – (48 + 18) = 120 – 66 = 54.
Since both conditions together yield a unique solution, they are 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.
(geometry) ABCD and AFGE are rectangles, and the area of ABCD is 120. What is the area of the rectangle AFGE?
1) The area of GBC is 24.
2) The area of EGD is 9.
Attachment:
12.11DS.png [ 9.68 KiB | Viewed 2624 times ]
=>
We can draw an additional line GH on the figure.
Attachment:
12.11DS(A).png [ 9.84 KiB | Viewed 2581 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) tells us that the area of rectangle BFHC is 48 since it is two times greater than the area of triangle GBC.
Condition 2) tells us that the area of rectangle EGHD is 18 since it is two times greater than the area of triangle EGD.
Then we have AFGE = ABCD – (FBCH + EGHD).
Since we have 4 variables (AFGE, ABCD, FBCH and EGHD) and 2 equations (ABCD = 120 and AFGE = ABCD – (FBCH + EGHD)), 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)
AFGE = ABCD – (FBCH + EGHD) = 120 – (48 + 18) = 120 – 66 = 54.
Since both conditions together yield a unique solution, they are 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.
