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Math Revolution DS Expert - Ask Me Anything about GMAT DS 11 Jul 2019, 01:08
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[GMAT math practice question]

(velocity) A river flows at \(a\) constant speed of \(2\) miles per hour. It takes \(3\) hours for a ship to go a miles upstream. How many hours does it take for the ship to go \(b\) miles downstream?

1) \(a = 6\) miles

2) \(b\) is longer than a by \(3\) miles
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 18 Sep 2021, 02:19
Originally posted by MathRevolution on 12 Jul 2019, 00:48.
Last edited by MathRevolution on 18 Sep 2021, 02:19, edited 1 time in total.
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[GMAT math practice question]

(inequality) Five consecutive integers satisfies \(a<b<c<d<e.\) what is the maximum of \(a+e\)?

1) the summation of five integers is negative

2) \(e\) is positive
Show more

=>

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.

Consecutive integers have two variables for the first number and the number of integers. Since the number of integers is \(5\), we need one more equation and D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
\(a + b + c + d + e = a + a + 1 + a + 2 + a + 3 + a + 4 = 5a + 10 < 0\) or \(a < -2.\) Then the maximum of a is \(-3\) and \(e = a + 4 = 1.\)

Thus the maximum value of \(a + e = (-3) + 1 = -2.\)

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
If \(e = 1\), then \(a = -3\) we have \(a + e = -2.\)

If \(e = 2,\) then \(a = -2\) we have \(a + e = 0.\)

If \(e = 3,\) then \(a = -1\) we have \(a + e = 2.\)
…
As \(e\) increases, \(a + e\) increases and approaches infinity.

Thus we don’t have a maximum value of \(a + e.\)

Condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 12 Jul 2019, 00:49
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[GMAT math practice question]

(Statistics) A class consists of \(30\) students. Among them \(a\) students have \(90\) books, \(b\) students have \(80\) books, \(c\) students have \(70\) books and all the remaining students have \(60\) books. What is the average number of books the students in the class have?

\(1) a= b+c\)

\(2) a\) is twice \(b\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 14 Nov 2021, 01:37
Originally posted by MathRevolution on 14 Jul 2019, 18:04.
Last edited by MathRevolution on 14 Nov 2021, 01:37, edited 1 time in total.
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[GMAT math practice question]

(velocity) A river flows at \(a\) constant speed of \(2\) miles per hour. It takes \(3\) hours for a ship to go a miles upstream. How many hours does it take for the ship to go \(b\) miles downstream?

1) \(a = 6\) miles

2) \(b\) is longer than a by \(3\) miles
Show more

=>

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.

Since we have \(2\) variables (\(a\) and \(b\)) and \(0\) equations, C is most likely to be 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)
The original speed of the ship is \(\frac{a}{3} + 2 = \frac{6}{3} + 2 = 4 mph.\) When the ship goes downstream, its speed is \(4 + 2 = 6 mph.\)

The time that the ship takes to travel b miles down stream is \(\frac{b}{6} = \frac{(a + 3)}{6} = \frac{(6 + 3 )}{6} = \frac{9}{6} = 1.5 hours.\)

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)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 14 Nov 2021, 01:39
Originally posted by MathRevolution on 14 Jul 2019, 18:06.
Last edited by MathRevolution on 14 Nov 2021, 01:39, edited 1 time in total.
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[GMAT math practice question]

(Statistics) A class consists of \(30\) students. Among them \(a\) students have \(90\) books, \(b\) students have \(80\) books, \(c\) students have \(70\) books and all the remaining students have \(60\) books. What is the average number of books the students in the class have?

\(1) a= b+c\)

\(2) a\) is twice \(b\)
Show more

=>

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.

Since we have \(3\) variables (\(a, b\) and \(c\)) and \(0\) equations, E is most likely to be 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)

The average number of books is
\(\frac{( 90a + 80b + 70c +60(30 – a – b – c) )}{30}\)

\(= \frac{( 30a + 20b + 10c + 1800)}{30}\)

If \(a = 2, b = 1\) and \(c = 1\), then the average is \(\frac{(60 + 20 + 10 + 1800)}{30} = \frac{1890}{30} = 63.\)

If \(a = 4, b = 2\) and \(c = 2\), then the average is \(\frac{(120 + 40 + 20 + 1800)}{30} = \frac{1980}{30} = 66.\)

Since both conditions together don’t yield a unique solution, they are not sufficient.
Therefore, E is the answer.
Answer: E

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 DS Expert - Ask Me Anything about GMAT DS 15 Jul 2019, 00:24
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[GMAT math practice question]

(geometry) What is \(d\)?

Attachment:
7.15.png
7.15.png [ 8.48 KiB | Viewed 1509 times ]

\(1) b=√3\)

\(2) c= 2\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 16 Jul 2019, 01:05
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[GMAT math practice question]

(algebra) What is \(a\)?

\(1) 3x-[7x-{2x-(5-6x)}] = -10x+4\)

\(2) –a+5 = 11x\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 17 Jul 2019, 01:30
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[GMAT math practice question]

(geometry) What is \(d\)?

Attachment:
7.15.png

\(1) b=√3\)

\(2) c= 2\)
Show more

=>

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. We then recheck the question. We should simplify conditions if necessary.

Remind that a \(30°-60°-90°\) right triangle has the ration among sides \(1:2: √3.\)

Condition 1)
We know all angles of the triangles, \(ABC\) and \(CDE.\) Since \(b = √3\), we can find \(CE =1, c = 2\) and \(BC = √3\). It follows that \(d = BC + CE = √3 + 1.\)

Thus, condition 1) is sufficient.

Condition 2)
We know all angles of the triangles, \(ABC\) and \(CDE\). Since \(c = 2\), we can find \(CE = 1\) and \(BC = √3.\) It follows that \(d = BC + CE = √3 + 1.\)

Thus, condition 2) is sufficient.

Therefore, D is the answer.
Answer: D
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 17 Jul 2019, 01:32
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[GMAT math practice question]

(algebra) \(\frac{m}{n}\) is a fraction. What are the values of \(m\) and \(n\)?

1) the irreducible form of \(\frac{m}{n}\) is \(\frac{3}{4}\)

2) if \(11\) is subtracted from numerator of \(\frac{m}{n}\) and \(4\) is added to denominator of \(\frac{m}{n}\), then the result is \(\frac{2}{5}\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 18 Sep 2021, 02:18
Originally posted by MathRevolution on 18 Jul 2019, 03:19.
Last edited by MathRevolution on 18 Sep 2021, 02:18, edited 1 time in total.
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[GMAT math practice question]

(algebra) What is \(a\)?

\(1) 3x-[7x-{2x-(5-6x)}] = -10x+4\)

\(2) –a+5 = 11x\)
Show more

=>

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.

Since we have \(2\) variables (\(a\) and \(x\)) and \(0\) equations, C is most likely to be 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) and 2)
\(3x-[7x-{2x-(5-6x)}] = 3x-[7x-{2x-5+6x}] = 3x-[7x-{8x-5}] = 3x-[7x-8x+5] = 3x-[-x+5] = 3x+x-5 = 4x – 5 = -10x + 4\)

Then, by condition 1), we must have \(14x = 9\) and \(x = \frac{9}{14}.\)

Since \(–a + 5 = 11x\), we have \(a = 5 -11x = 5 -11(\frac{9}{14}) = -(\frac{29}{14})\)

Thus, both conditions together 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.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 18 Jul 2019, 03:20
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[GMAT math practice question]

(algebra) Let \(x\) be a real number. \((a, b)\) denotes \(ax+b\). What is \((1, 0)\)?

\(1) 3*(2,0)=(-1, 4) – (-2, -6)\)

\(2) (1, 0)^2 +4 = 4(1, 0)\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 13 Sep 2021, 02:35
Originally posted by MathRevolution on 19 Jul 2019, 01:04.
Last edited by MathRevolution on 13 Sep 2021, 02:35, edited 1 time in total.
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[GMAT math practice question]

(algebra) \(\frac{m}{n}\) is a fraction. What are the values of \(m\) and \(n\)?

1) the irreducible form of \(\frac{m}{n}\) is \(\frac{3}{4}\)

2) if \(11\) is subtracted from numerator of \(\frac{m}{n}\) and \(4\) is added to denominator of \(\frac{m}{n}\), then the result is \(\frac{2}{5}\)
Show more

=>

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.


Since we have \(2\) variables (\(x\) and \(y\)) and \(0\) equations, C is most likely to be 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) and 2)
Using condition 1), \(\frac{m}{n} = \frac{3}{4}\), we must have \(4m = 3n.\)

Condition 2) tells us that \(\frac{( m – 11 )}{( n + 4 )} = \frac{2}{5}\). Thus, \(5(m-11) = 2(n+4)\) and \(5m – 55 = 2n + 8.\) Rearranging yields \(5m = 2n + 63\) and \(15m = 6n + 189\).

Since \(6n = 8m, 15m = 8m + 189\), and \(7m = 189\). Thus, \(m = 27\) and \(n = 36.\)

Both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 19 Jul 2019, 01:04
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[GMAT math practice question]

(number properties) \(a\) and \(b\) are positive integers. What is the value of \(b-a\)?

\(1) \frac{a}{b} = \frac{2}{7}\)

\(2) a+b\) is a two-digit integer greater than \(20\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 13 Sep 2021, 02:36
Originally posted by MathRevolution on 21 Jul 2019, 18:42.
Last edited by MathRevolution on 13 Sep 2021, 02:36, edited 1 time in total.
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[GMAT math practice question]

(algebra) Let \(x\) be a real number. \((a, b)\) denotes \(ax+b\). What is \((1, 0)\)?

\(1) 3*(2,0)=(-1, 4) – (-2, -6)\)

\(2) (1, 0)^2 +4 = 4(1, 0)\)
Show more

=>

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. We then recheck the question. We should simplify conditions if necessary.

Since \((1, 0)=1*x+0=x\), the question asks for the value of \(x\).

Since we have \(1\) variable \((x)\) and \(0\) equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
The left hand side is \(3*(2,0) = 3*(2x + 0) = 6x\) and the right hand side evaluates to \((-1,4) – (-2,-6) = -x + 4 – (-2x – 6) = x + 10.\)
Equating both sides yields \(6x = x + 10\) and \(x = 2.\)

Thus, condition 1) is sufficient.

Condition 2)
\((1,0)^2 + 4 = 4(1,0)\)

\(=> (x)^2 + 4 =4(x)\)

\(=> x^2 -4x + 4 = 0\)

\(=> (x-2)^2 = 0\)

\(=> x = 2.\)

Thus, condition 2) is also sufficient.

Therefore, D is the answer.
Answer: D

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 29 Sep 2021, 01:23
Originally posted by MathRevolution on 21 Jul 2019, 18:44.
Last edited by MathRevolution on 29 Sep 2021, 01:23, edited 1 time in total.
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[GMAT math practice question]

(number properties) \(a\) and \(b\) are positive integers. What is the value of \(b-a\)?

\(1) \frac{a}{b} = \frac{2}{7}\)

\(2) a+b\) is a two-digit integer greater than \(20\)
Show more

=>

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.

Since we have \(2\) variables (\(a\) and \(b\)) and \(0\) equations, C is most likely to be 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 \(\frac{a}{b}= \frac{2}{7}\), we have \(7a = 2b.\)

If \(a = 4\) and \(b = 14\), then \(\frac{a}{b} = \frac{4}{14} = \frac{2}{7}, a+ b = 21 > 20\), and \(b – a = 10.\)

If \(a = 6\) and \(b = 21\), then \(\frac{a}{b} = \frac{6}{21} = \frac{2}{7}, a + b = 27 > 20,\) and \(b – a = 15.\)

Since both conditions together don’t yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E

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.

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 DS Expert - Ask Me Anything about GMAT DS 22 Jul 2019, 18:47
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[GMAT math practice question]

(geometry) \(ABCD\) and \(AFGE\) are rectangles and the area of rectangle \(ABCD\) is \(120\). What is the area of rectangle \(AFGE\)?

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1) the area of triangle \(GBC\) is \(24\)
2) the area of triangle \(EGD\) is \(9\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 23 Jul 2019, 01:45
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[GMAT math practice question]

(geometry) In the figure, lines \(AB, CD\) and \(EF\) are parallel, and lines \(BC\) and \(DE\) are parallel. What is the length of \(CD\)?

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\(1) AB=3\)

\(2) EF=12\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 24 Jul 2019, 01:09
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[GMAT math practice question]

(geometry) \(ABCD\) and \(AFGE\) are rectangles and the area of rectangle \(ABCD\) is \(120\). What is the area of rectangle \(AFGE\)?

Attachment:
The attachment 7.22.png is no longer available

1) the area of triangle \(GBC\) is \(24\)
2) the area of triangle \(EGD\) is \(9\)
Show more

=>

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. We then recheck the question. We should simplify conditions if necessary.

Since finding the area of a rectangle requires \(2\) variables, C is most likely to be 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)

Attachment:
a.png
a.png [ 7.67 KiB | Viewed 1370 times ]

Let \(H\) be the point of intersection of the extension of \(FG\) with side \(CD\). Since the area of rectangle \(BCHF\) is twice the area of triangle \(GBC\), condition 1) tells us that the area of rectangle \(BCHF\) is \(48\). Since the area of rectangle \(EDGH\) is twice the area of triangle \(EGD\), condition 2) tells us that the area of rectangle \(EDGF\) is \(18.\)
Now, the area of rectangle \(AFGE\) is the area of rectangle \(ABCD\) minus the sum of the areas of rectangles \(BCHF\) and \(EDGH\). It is \(120 – ( 48 + 18 ) = 120 – 66 = 54.\)

Therefore, C is the answer.
Answer: C
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 24 Jul 2019, 01:09
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[GMAT math practice question]

(geometry) \(l\) is parallel to \(m\), what is the value of \(x+y\)?

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\(1) A=100^o\)

\(2) B=50^o\)
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Math Revolution DS Expert - Ask Me Anything about GMAT DS 25 Jul 2019, 01:24
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[GMAT math practice question]

(geometry) In the figure, lines \(AB, CD\) and \(EF\) are parallel, and lines \(BC\) and \(DE\) are parallel. What is the length of \(CD\)?

Attachment:
7.23.png

\(1) AB=3\)

\(2) EF=12\)
Show more

=>

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. We then recheck the question. We should simplify conditions if necessary.

Triangles \(ABC\) and \(CDE\) are similar, and triangles \(BDC\) and \(DFE\) are similar. So, we can set up the proportion \(AB:CD = CD:EF.\)

Since \(CD^2 = AB*EF\), conditions 1) and 2) together give us sufficient information to calculate the value of \(CD\).

Therefore, C is the answer.
Answer: C
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