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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

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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
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[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

=>

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.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

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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 $$b$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[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

=>

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 $$\frac{b}{6} = \frac{(a + 3)}{6} = \frac{(6 + 3 )}{6} = \frac{9}{6} = 1.5 hours.$$

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)
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[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 $$b$$

=>

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.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[GMAT math practice question]

(geometry) What is $$d$$?

Attachment: 7.15.png [ 8.48 KiB | Viewed 251 times ]

$$1) b=√3$$

$$2) c= 2$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[GMAT math practice question]

(algebra) What is $$a$$?

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

$$2) –a+5 = 11x$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

(geometry) What is $$d$$?

Attachment:
7.15.png

$$1) b=√3$$

$$2) c= 2$$

=>

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.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[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 $$\frac{2}{5}$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

(algebra) What is $$a$$?

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

$$2) –a+5 = 11x$$

=>

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.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[GMAT math practice question]

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

$$1) 3*(2,0)=(-1, 4) – (-2, -6)$$

$$2) (1, 0)^2 +4 = 4(1, 0)$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[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 $$\frac{2}{5}$$

=>

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.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[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 $$20$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

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

$$1) 3*(2,0)=(-1, 4) – (-2, -6)$$

$$2) (1, 0)^2 +4 = 4(1, 0)$$

=>

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.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[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 $$20$$

=>

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.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[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: 7.22.png [ 7.6 KiB | Viewed 141 times ]

1) the area of triangle $$GBC$$ is $$24$$
2) the area of triangle $$EGD$$ is $$9$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[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 [ 14.87 KiB | Viewed 132 times ]

$$1) AB=3$$

$$2) EF=12$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[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 $$9$$

=>

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 [ 7.67 KiB | Viewed 113 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 $$120 – ( 48 + 18 ) = 120 – 66 = 54.$$

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

[GMAT math practice question]

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

Attachment: 7.24q.png [ 12.84 KiB | Viewed 112 times ]

$$1) A=100^o$$

$$2) B=50^o$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8261
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[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

$$1) AB=3$$

$$2) EF=12$$

=>

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 $$CD$$.

_________________ Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS   [#permalink] 25 Jul 2019, 01:24

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# Math Revolution DS Expert - Ask Me Anything about GMAT DS  