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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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[GMAT math practice question]

(number properties) $$a$$ and $$b$$ are positive integers. What is the remainder when $$b$$ is divided by $$4$$?

1) if $$a$$ is divided by $$4,$$ the remainder is $$3$$

2) if $$a^2+b$$ is divided by $$4$$, the remainder is $$1$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

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

Attachment:
7.24q.png

$$1) A=100^o$$

$$2) B=50^o$$

=>

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.

$$<x = <A + <B$$ and $$<y = 180 - <A.$$

Therefore, $$x + y = <A + <B + 180 - <A = <B + 180.$$

Thus, condition 2) is sufficient on its own.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(number properties) $$p, q$$ and $$r$$ are prime numbers. What is the value of $$p$$?

$$1) p+q=r$$

$$2) 1<p<q$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(number properties) $$a$$ and $$b$$ are positive integers. What is the remainder when $$b$$ is divided by $$4$$?

1) if $$a$$ is divided by $$4,$$ the remainder is $$3$$

2) if $$a^2+b$$ is divided by $$4$$, the remainder is $$1$$

=>

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.

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)
Condition 1) tells us that $$a$$ has remainder $$3$$, when it is divided by $$4$$. So, $$a^2$$ has remainder $$1$$, when it is divided by $$4.$$

Condition 2) tells us that $$a^2+b$$ has remainder $$1$$ when it is divided by $$4$$. Since $$a^2$$ has remainder $$1$$ when it is divided by $$4, b$$ has remainder $$0$$ when it is divided by $$4.$$

Thus, both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since there is no information about $$b$$ in condition 1), it is not sufficient.

Condition 2)
If $$a = 1$$ and $$b = 4$$, then $$b$$ has remainder $$0$$ when it is divided by $$4.$$

If $$a = 4$$ and $$b = 1,$$ then $$b$$ has remainder $$1$$ when it is divided by $$4.$$

Condition 2) is not sufficient since it does not yield a unique answer.

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: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(number properties) $$p, q$$ and $$r$$ are prime numbers. What is the value of $$p$$?

$$1) p+q=r$$

$$2) 1<p<q$$

=>

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 ($$p, q$$ and $$r$$) 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)
Since $$p + q = r$$ and $$p, q$$ and $$r$$ are prime numbers, one of $$p$$ and $$q$$ must be $$2.$$

In addition, $$p = 2$$ because $$1 < p < q.$$

Both conditions together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If $$p = 2, q = 3$$ and $$r = 5$$, then $$p = 2.$$

If $$p = 3, q = 2$$ and $$r = 5$$, then $$p = 3.$$

Since condition 1) doesn’t yield a unique solution, it is not sufficient.

Condition 2)
If $$p = 2$$ and $$q = 3$$, then $$p = 2.$$

If $$p = 3$$ and $$q = 5,$$ then $$p = 3.$$

Since condition 2) doesn’t yield a unique solution, it is not 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: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(geometry) In the figure, $$AB$$ is parallel to $$EF.$$ What is the value of $$z$$?

Attachment: 7.29ds.png [ 8.92 KiB | Viewed 282 times ]

$$1) x =78^o$$

$$2) y = 70^o$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(number properties) $$n$$ is a positive integer. What is the value of $$n$$?

1) $$n+200$$ is a perfect square

2) $$n+292$$ is a perfect square
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(geometry) In the figure, $$AB$$ is parallel to $$EF.$$ What is the value of $$z$$?

Attachment:
The attachment 7.29ds.png is no longer available

$$1) x =78^o$$

$$2) y = 70^o$$

=>

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 ($$x, y$$ and $$z$$) 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.

Attachment: 7.31.png [ 22.29 KiB | Viewed 234 times ]

Conditions 1) & 2)
We draw lines through $$C$$ and $$D$$, parallel to $$AB$$, as shown in the diagram.
Since $$<a$$ and $$<ABC=105°$$ are supplementary, $$a=75°$$.
$$<d = 180° - <X - <a = 180° - 78° - 75° = 27°$$, and $$<c = <d = 27°$$ as they are alternate interior angles.
Since $$y = 70°, b = y – c = 70°-27° = 43°$$
Since $$<z$$ and $$<b$$ are alternate interior angles, $$<z = <b =43°.$$
Both conditions together are sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(number properties) $$n$$ is a positive integer. What is the value of $$n$$?

1) $$n$$ is less than $$200$$

2) the number of positive factors of $$n$$ is $$15$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

(number properties) $$n$$ is a positive integer. What is the value of $$n$$?

1) $$n+200$$ is a perfect square

2) $$n+292$$ is a perfect square

=>

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

Condition 1)
If $$n + 200 = 400 = 20^2$$, then $$n = 200.$$

If $$n + 200 = 441 = 21^2,$$ then $$n = 241.$$

Since condition 1) does not yield a unique answer, it is not sufficient.

Condition 2)
If $$n + 292 = 400 = 20^2,$$ then $$n = 108.$$

If $$n + 292 = 441 = 21^2,$$ then $$n = 149.$$

Since condition 2) does not yield a unique answer, it is not sufficient.

Conditions 1) & 2)
Write $$n + 200 = a^2$$ and $$n + 292 = b^2,$$ for some positive integers $$a$$ and $$b$$. Then

$$b^2 – a^2 = (n+292)-(n+200) = 92 = 2^2*23$$ and

$$(b+a)(b-a) = 2^2*23$$

Since $$b + a$$ and $$b – a$$ have the same parity, which means both $$b + a$$ and $$b – a$$ are even or both $$b + a$$ and $$b – a$$ are odd, $$b + a = 46$$ and $$b – a = 2$$.

Solving these equations simultaneously yields $$a = 22$$ and $$b = 24.$$

Thus $$n = 24^2 – 292 = 284.$$

The two conditions are sufficient, when applied together.

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: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(number properties) $$A$$ and $$B$$ are one-digit numbers. What is the value of $$A+B$$?

1) The $$6$$ six-digit integer $$B6354A$$ is a multiple of $$99$$

2) $$A$$ is less than $$B$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

(number properties) $$n$$ is a positive integer. What is the value of $$n$$?

1) $$n$$ is less than $$200$$

2) the number of positive factors of $$n$$ is $$15$$

=>

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 $$1$$ variable ($$n$$) and $$0$$ equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1) is obviously not sufficient.

Condition 2)
If $$n$$ has $$15$$ factors, then $$n = p^4*q^2$$ or $$n=p^{14}$$, where $$p$$ and $$q$$ are prime numbers.
Condition 2) is not sufficient, since there are a lot of possibilities.

Conditions 1) & 2)
If $$p = 2$$ and $$q = 3$$ and $$n = p^4*q^2$$, then $$n = (2^4)(3^2) = 144$$. Note that $$2^14 = 16384 > 200$$ and $$3^4 2^2 = 324 > 200$$, so this is the only possible value of $$n$$ satisfying conditions 1) and 2). For example, if $$p = 2$$ and $$q = 5$$, then $$n = 400.$$

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: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

[GMAT math practice question]

(algebra) What is the value of $$\frac{(a-b)}{(a+b)} –ab + \frac{b}{c}$$ ?

$$1) a=bc$$

$$2) a=\frac{1}{2}$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(number properties) $$A$$ and $$B$$ are one-digit numbers. What is the value of $$A+B$$?

1) The $$6$$ six-digit integer $$B6354A$$ is a multiple of $$99$$

2) $$A$$ is less than $$B$$

=>

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 $$2$$ 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)
Condition 1) tells us that $$B6354A$$ is a multiple of $$9$$. So, $$A + B + 6 + 3 + 5 + 4 = A + B + 18$$ is a multiple of $$9$$, and $$A + B$$ is a multiple of $$9$$.

The possible pairs $$(A,B)$$ are $$(0,9), (1,8), (2,7), … , (8,1)$$ and $$(9,9).$$

Since condition 2) tells us that $$A < B, (9,9)$$ is not possible. For all remaining pairs, the value of of $$A + B$$ is $$9.$$

Therefore, conditions 1) and 2) are sufficient, when applied together.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since $$B6354A$$ is a multiple of $$9$$ and $$A + B + 6 + 3 + 5 + 4 = A + B + 18$$ is a multiple of $$9, A + B$$ is a multiple of $$9.$$

The possible pairs $$(A,B)$$ are $$(0,9), (1,8), (2,7), … , (8,1)$$ and $$(9,9).$$

We test these pairs individually to check whether they give rise to multiples of $$99$$:
$$963540 = 11*87594 + 6$$ is not a multiple of $$11.$$

$$863541 = 11*78503 + 8$$ is not a multiple of $$11.$$

$$763532 = 11*69412 + 10$$ is not a multiple of $$11.$$

$$663543 = 11*60322 + 1$$ is not a multiple of $$11.$$

$$563544 = 11*51231 + 3$$ is not a multiple of $$11.$$

$$463545 = 11*42140 + 5$$ is not a multiple of $$11.$$

$$363546 = 11*33049 + 7$$ is not a multiple of $$11.$$

$$263547 = 11*23958 +$$9 is not a multiple of $$11.$$

$$163548 = 11*14868$$ is a multiple of $$11.$$

$$963549 = 11*87595 + 4$$ is not a multiple of $$11.$$

$$(8,1)$$ is a unique pair of $$(A,B)$$.
Than we have $$A + B = 9.$$

Condition 1) is sufficient, since it yields a unique solution.

Condition 2) is obviously not sufficient.

_________________

Originally posted by MathRevolution on 04 Aug 2019, 18:50.
Last edited by MathRevolution on 10 Aug 2019, 07:39, edited 2 times in total.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

(algebra) What is the value of $$\frac{(a-b)}{(a+b)} –ab + \frac{b}{c}$$ ?

$$1) a=bc$$

$$2) a=\frac{1}{2}$$

=>

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.

Since we have $$3$$ variables ($$x, y$$ and $$z$$) 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)
Plugging in $$a = bc = \frac{1}{2}$$ yields

$$\frac{(a-b)}{(a+b)} – ab + \frac{b}{c} = \frac{(bc-b)}{(bc+b)} – b^2c + \frac{b}{c} = \frac{b(c-1)}{b(c+1)} – (\frac{1}{2})c + \frac{(bc)}{c^2} = \frac{(c-1)}{(c+1)} – \frac{1}{2c} + \frac{1}{(2c^2)}.$$

Since we don’t know the value of $$c$$, both conditions together don’t yield a unique solution and 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: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(algebra) What is the value of $$\frac{(2x)}{(x+y)} + \frac{(3y)}{(x-y)} +\frac{(x^2)}{(x^2 – y^2)}$$?

$$1) \frac{x}{2} = \frac{y}{3}$$

$$2) x=1$$
_________________

Originally posted by MathRevolution on 05 Aug 2019, 01:13.
Last edited by MathRevolution on 07 Aug 2019, 03:09, edited 1 time in total.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

[GMAT math practice question]

(algebra) What is the value of $$\frac{(3mr-nt)}{(4nt-7mr)}$$?

$$1) \frac{m}{n} = \frac{4}{3}$$

$$2) \frac{r}{t}= \frac{9}{14}$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

(algebra) What is the value of $$\frac{(2x)}{(x+y)} + \frac{(3y)}{(x-y)} +\frac{(x^2)}{(x^2 – y^2)}$$?

$$1) \frac{x}{2} = \frac{y}{3}$$

$$2) x=1$$

=>

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.

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 the conditions if necessary.

$$\frac{(2x)}{(x+y)} + \frac{(3y)}{(x-y)} +\frac{(x^2)}{(x^2 – y^2)}$$

$$= \frac{(2x)(x-y)}{(x+y)(x-y)} + \frac{(3y)(x+y)}{(x-y)(x+y)} +\frac{(x^2)}{(x^2 – y^2)}$$

$$= \frac{(2x)(x-y)}{(x^2 – y^2)} + \frac{(3y)(x+y)}{(x^2 – y^2)} +\frac{(x^2)}{(x^2 – y^2)}$$

$$= \frac{{(2x)(x-y) + (3y)(x+y) +(x^2)}}{(x^2 – y^2)}$$

$$= \frac{( 3x^2 +xy + 3y^2 )}{(x^2 – y^2)}$$

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that A is most likely to be the answer to this question.

Condition 1)
Rearranging $$\frac{x}{2} = \frac{y}{3}$$ yields $$x = (\frac{2}{3})y.$$

Therefore,
$$\frac{( 3x^2 +xy + 3y^2 )}{(x^2 – y^2)} = (3*(\frac{2}{3})^2y^2 + (\frac{2}{3})y^2 + 3y^2) / ((\frac{2}{3})^2y^2 – y^2)$$

$$= ((\frac{4}{3}) + (\frac{2}{3}) + 3)y^2 / ((\frac{4}{9}) – 1)y^2$$

$$= 5y^2 / (\frac{-5}{9})y^2$$

$$= 9$$

Thus, condition 1) alone is sufficient.

Condition 2) is obviously not sufficient since it provides no information about $$y$$.

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that A is most likely to be the answer to this question.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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[GMAT math practice question]

(number property) What are the values of $$x$$ and $$y$$?

$$1) \frac{1}{x} + \frac{1}{y} = \frac{1}{5}$$

2) $$x$$ and $$y$$ are positive integers
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(algebra) What is the value of $$\frac{(3mr-nt)}{(4nt-7mr)}$$?

$$1) \frac{m}{n} = \frac{4}{3}$$

$$2) \frac{r}{t}= \frac{9}{14}$$

=>

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 the conditions if necessary.

We rearrange $$\frac{(3mr-nt)}{(4nt-7mr)}$$ to see if we can write in terms of the ratios m/n and r/t given in the conditions:
$$\frac{(3mr-nt)}{(4nt-7mr)}$$
$$= ( \frac{(3mr)}{(nt)} – \frac{(nt}{nt)} ) / ( 4\frac{(nt}{nt)} – 7\frac{mr}{nt} )$$
$$= ( 3(\frac{m}{n})*(\frac{r}{t}) – 1 ) / ( 4 – 7(\frac{m}{n})(\frac{r}{t}) )$$

Now, both conditions 1) & 2) together are sufficient since the simplified question requires only the values of $$(\frac{m}{n})$$ and $$(\frac{r}{t})$$.

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