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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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Vinit1 wrote:
MathRevolution wrote:

Condition 2)
If $$x = 2$$ and $$y = 2$$, then $$y$$ is divisible by $$x$$ and the answer is 'yes'.
If $$x = 4$$ and $$y = 2$$, then $$y$$ is not divisible by $$x$$ and the answer is 'no'.
Since condition 2) does not yield a unique answer, it is not sufficient.

But, 2 and 4 do not have the same prime factors. 2 has only 1 2, and 4 has 2 2s. 2^2 cannot be same as 2 right?

If the question said same UNIQUE prime factors, then this answer would be correct.

If what you say is correct, then can I assume that whenever a question says PRIME FACTORS, it means UNIQUE PRIME FACTORS?

Posted from my mobile device

PS: I also checked with the original source, and they agreed that it was a mistake in their problem. The problem should have specified unique prime factors.

$$4$$ has a prime factor $$2$$ since $$4 = 2^2$$ and $$2$$ has a prime factor $$2$$.
Thus $$4$$ and $$2$$ have the same prime factor $$2$$.
They satisfy condition 2).

Prime factors do not mean unique prime factors.

Another examples are $$12$$ and $$18$$.
Since $$12 = 2^2 \cdot 3^1$$, $$12$$ has prime factors $$2$$ and $$3$$.
Since $$18 = 2^1 \cdot 3^1$$, $$18$$ has prime factors $$2$$ and $$3$$.
Thus, $$12$$ and $$18$$ have the same prime factors $$2$$ and $$3$$.
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Good Evening,

My question pertains to the inequality problems, where we can't solve by adding or subtracting Statement 1 and Statement 2 and we need to pick numbers to check, how to approach those problems as there are high chances to miss certain values(such as fractions between -1 and 0 OR similar) and pick a wrong trap answer? The question is a bit general in nature but I hope you understand the issue at hand. I appreciate any suggestion/approach.

Thanks.
DV
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(algebra) What is the value of $$x$$?

$$1) [x, y, z]=xy+yz+zx$$

$$2) [1, x, 2]=[4, -3, 2].$$

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have $$3$$ variables ($$x, y,$$ and $$z$$) and $$0$$ equations, E 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)
Condition 2) tells us that $$[1, x, 2]=[4, -3, 2]$$. Substituting $$1, x, 2$$ into $$xy + yz + zx$$ and then substituting $$4, -3, 2,$$ into $$xy + yz + zx$$ gives us $$(1)(x) + (x)(2) + (2)(1) = (4)(-3) + (-3)(2) + (2)(4)$$, which simplifies to $$x + 2x + 2 = -12 – 6 + 8$$ or $$3x = -12.$$

So, we have $$x = -4,$$ and both conditions together are sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(functions) $$f(x)○f(y)$$ is defined as $$f(x+y+2xy)$$. What is the value of $$1○(-1)$$?

$$1) f(-1)=-1$$ and $$f(0)=1$$

$$2) f(x)=2x+1$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(algebra) $$abc ≠ 0$$. What is the value of $$a(\frac{1}{b} + \frac{1}{c}) +b(\frac{1}{c} + \frac{1}{a}) + c(\frac{1}{a} + \frac{1}{b})$$?

$$1) |a+b+c| ≤ 0$$

$$2) a+b+c = 0$$

=>

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.
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.

So, we will first simply the original condition as follows:

$$a(\frac{1}{b} + \frac{1}{c}) +b(\frac{1}{c} + \frac{1}{a}) + c(\frac{1}{a} + \frac{1}{b})$$
$$= \frac{a}{b} + \frac{a}{c} + \frac{b}{c} + \frac{b}{a} + \frac{c}{a} + \frac{c}{b}$$
$$= \frac{(b+c)}{a} + \frac{(a+c)}{b} + \frac{(a+b)}{c}$$
$$= \frac{(a+b+c-a)}{a} + \frac{(a+b+c-b)}{b} + \frac{(a+b+c-c)}{c}$$
$$= \frac{(a+b+c)}{a} – \frac{a}{a} + \frac{(a+b+c)}{b} – \frac{b}{b} + \frac{(a+b+c)}{c} – \frac{c}{c}$$
$$= (a+b+c)[(\frac{1}{a})+(\frac{1}{b})+(\frac{1}{c})] – 3$$
If $$a+b+c= 0,$$ then we have $$(a+b+c)[(\frac{1}{a})+(\frac{1}{b})+(\frac{1}{c})] – 3 = -3.$$

Condition 1)
$$|a+b+c|≤0$$ means $$a+b+c=0$$ since $$|a+b+c|≥0$$
So, we have a$$(\frac{1}{b} + \frac{1}{c}) +b(\frac{1}{c} + \frac{1}{a}) + c(\frac{1}{a} + \frac{1}{b}) = -3.$$
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since we have $$a+b+c=0$$, we have a$$(\frac{1}{b} + \frac{1}{c}) +b(\frac{1}{c} + \frac{1}{a}) + c(\frac{1}{a} + \frac{1}{b}) = -3.$$
Since condition 2) yields a unique solution, it is also sufficient.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(functions) What is the value of $$\frac{f(2)}{f(1)} + \frac{f(3)}{f(2)} + \frac{f(4)}{f(3)} + … +\frac{f(2006)}{f(2005)}$$?

$$1) f(1)=1$$

$$2) f(a+b)=f(a)f(b)$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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1
MathRevolution wrote:
[GMAT math practice question]

(functions) $$f(x)○f(y)$$ is defined as $$f(x+y+2xy)$$. What is the value of $$1○(-1)$$?

$$1) f(-1)=-1$$ and $$f(0)=1$$

$$2) f(x)=2x+1$$

=>

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.

Since we have many variables to determine a function and $$0$$ equations, E is most likely to be the answer. However, by Tip 1) of the VA method, D is most likely to be the answer if condition 1) gives the same information as condition 2).

Condition 1)
$$1○(-1) = f(0)○f(-1)=f(0+(-1)+0)=f(-1)=-1.$$

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

Condition 2)
Since we have $$f(0)=1$$ and $$f(-1)=-1,$$ we have $$1○(-1) = f(0)○f(-1)=f(0+(-1)+0)=f(-1)=-1.$$

Since condition 2) yields a unique solution, it is sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(number properties) $$f(x)$$ denotes the maximum prime factor of $$x$$, where $$x$$ is a positive integer. For example, $$f(30)=f(2*3*5)=5.$$ What is the value of $$f(abc)$$?

$$1) f(a) = 2$$

$$2) f(b)+f(c)=14$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(functions) What is the value of $$\frac{f(2)}{f(1)} + \frac{f(3)}{f(2)} + \frac{f(4)}{f(3)} + … +\frac{f(2006)}{f(2005)}$$?

$$1) f(1)=1$$

$$2) f(a+b)=f(a)f(b)$$

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have many variables to determine a function 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 we have $$f(2)=f(1+1)=f(1)f(1)$$, we have $$\frac{f(2)}{f(1)} = \frac{f(1)f(1)}{f(1)} = f(1)$$

Since we have $$f(3)=f(2+1)=f(2)f(1)$$, we have $$\frac{f(3)}{f(2)} = \frac{f(2)f(1)}{f(2)} = f(1)$$

Since we have $$f(4)=f(3+1)=f(3)f(1)$$, we have $$\frac{f(4)}{f(3)} = \frac{f(3)f(1)}{f(3)} = f(1)$$

Since we have $$f(2006)=f(2005+1)=f(2005)f(1)$$, we have $$\frac{f(2006)}{f(2005)} = f(1)$$

So, we have $$\frac{f(2)}{f(1)} + \frac{f(3)}{f(2)} + \frac{f(4)}{f(3)} + … +\frac{f(2006)}{f(2005)} = f(1) + f(1) + … + f(1) = 2005*f(1) = 2005.$$

Both conditions together yield a unique solution, so they are sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(number properties) $$f(x)$$ denotes the maximum prime factor of $$x$$, where $$x$$ is a positive integer. For example, $$f(30)=f(2*3*5)=5.$$ What is the value of $$f(abc)$$?

$$1) f(a) = 2$$

$$2) f(b)+f(c)=14$$

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have $$3$$ variables 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)

If $$a = 2, b = 7$$ and $$c = 7$$, then $$f(abc) = f(2*7^2) = 7$$.
If $$a = 2, b = 3$$ and $$c = 11$$, then$$f(abc) = f(2*3*11) = 11.$$
Both conditions together do not yield a unique solution, so 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 when the answer is A, B, C, or D.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(function) What is the value of $$f(3)+f(2)$$?

$$1) f(a)f(b) = 3f(a+b)+f(a-b)$$

$$2) f(1) = 5$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(function) $$f(x)$$ is a function. What is the value of $$a$$?

$$1) f(a)+ 4f(\frac{1}{a})=15a$$

$$2) f(a)=f(-a)$$
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(function) What is the value of $$f(3)+f(2)$$?

$$1) f(a)f(b) = 3f(a+b)+f(a-b)$$

$$2) f(1) = 5$$

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have many variables to determine a function 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)
If $$a = 1$$, and $$b = 0$$, then we have $$f(1)f(0) = 3f(1+0) + f(1-0) = 4f(1) = 4(5) = 20$$ or $$5f(0) = 20.$$ So, we have $$f(0) = 4.$$

If $$a = 1$$, and $$b = 1$$, then we have $$f(1)f(1) = 3f(1+1) + f(1-1) = 3f(2) + f(0) = 3f(2) + 4.$$ Therefore $$3f(2) + 4 = 25, 3f(2) = 21$$, or $$f(2) = 7.$$

If $$a = 2, b = 1,$$ then we have $$f(2)f(1) = 3f(2+1) + f(2-1) = 3f(3) + f(1) = 3f(3) + 5.$$
Therefore $$3f(3) + 5 = 5*7, 3f(3) + 5 = 35, 3f(3) = 30,$$ or $$f(3) = 10.$$

Then, $$f(3)+f(2) = 10 + 7 = 17.$$

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 when the answer is A, B, C, or D.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(statistics) In a basketball game, Watson, a new player, substitutes in for James. What is the height of James?

1) The height of Watson is 192 cm.
2) After the substitution, the average height of the 5 players increased by 1.8 cm.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(function) $$f(x)$$ is a function. What is the value of $$a$$?

$$1) f(a)+ 4f(\frac{1}{a})=15a$$

$$2) f(a)=f(-a)$$

=>

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.

Since we have many variables to determine a function 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)
When we substitute a by $$\frac{1}{a}$$ in condition 1), we have $$f(\frac{1}{a}) + 4f(a) = 15(\frac{1}{a})$$ or $$4f(\frac{1}{a})+16f(a) = 60(\frac{1}{a}).$$

Then, since we have $$4f(\frac{1}{a}) = 15a – f(a)$$ from condition 1), we have $$4f(\frac{1}{a}) + 16f(a) = (15a – f(a)) + 16f(a) = 15f(a) + 15a = \frac{60}{a}$$ or $$f(a) = -a + \frac{4}{a}.$$

When we substitute a by $$–a$$, we have $$f(-a) = a – \frac{4}{a}$$ and $$–a + \frac{4}{a} = a – \frac{4}{a}.$$

Then, we have $$a = \frac{4}{a}$$ or $$a^2 = 4$$ and we have solutions $$a = 2$$ or $$-2$$.

Since both conditions do not 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 when the answer is A, B, C, or D.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(geometry) $$AB$$ is a straight line. What is the measure of the angle $$∠AOD$$?

$$1) ∠EOB = (\frac{4}{5})∠AOD$$

$$2) ∠DOE = \frac{∠AOB}{2}$$

Attachment: 10.10.png [ 10.83 KiB | Viewed 113 times ]

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

MathRevolution wrote:
[GMAT math practice question]

(statistics) In a basketball game, Watson, a new player, substitutes in for James. What is the height of James?

1) The height of Watson is 192 cm.
2) After the substitution, the average height of the 5 players increased by 1.8 cm.

=>

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.

Assume j is James’ height, and w is Watson’s height.

Since we have $$2$$ variables ($$j$$ and $$w$$) and $$0$$ equations, 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)
We have $$w = 192$$ and $$\frac{( w – j )}{5} = 1.8$$ which is the increased height after the substitution.

We have $$w – j =9$$ and $$j = w – 9, j = 192 – 9$$, and $$j = 183.$$

Since both conditions together yield a sufficient condition, C appears to be the solution.

Since this question is a statistics 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)
We have $$w = 192$$, but condition 1) does not give us any information about $$w$$.
Condition 1) is obviously not sufficient.

Condition 2)
We have $$j = w – 9.$$
Since condition 2) does not 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: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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[GMAT math practice question]

(algebra) What is the length of $$BE$$?

1) $$AB = 24cm$$ and $$C$$ is the midpoint of $$AB$$

2)$$AD+CE = 5, AD = \frac{CD}{3}$$

Attachment: 10.11ds.png [ 4.72 KiB | Viewed 88 times ]

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(geometry) $$AB$$ is a straight line. What is the measure of the angle $$∠AOD$$?

$$1) ∠EOB = (\frac{4}{5})∠AOD$$

$$2) ∠DOE = \frac{∠AOB}{2}$$

Attachment:
10.10.png

=>

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.

Assume $$<AOD = x, <DOE = y$$ and $$<EOB = z.$$

Then we have $$x + y + z = 180.$$

Since we have $$3$$ variables ($$x, y$$ and $$z$$) and $$1$$ equation ($$x + y + z = 180$$), 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)
We have $$z = (\frac{4}{5})x$$ from condition 1) and $$y = 90$$ from condition 2).
Then we have $$x + z = 90$$ and $$x + (\frac{4}{5})x = 90$$, or $$(\frac{9}{5})x = 90.$$
Then, $$x = 50.$$

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: 8243
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[GMAT math practice question]

(algebra) What is the length of $$BE$$?

1) $$AB = 24cm$$ and $$C$$ is the midpoint of $$AB$$

2)$$AD+CE = 5, AD = \frac{CD}{3}$$

Attachment:
10.11ds.png

=>

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.

Since we have $$4$$ variables ($$AD, DC, CE$$, and $$EB$$) and $$0$$ equations and each condition has $$2$$ 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)
We have $$AD + DC + CE + EB = 24$$ and $$CE + EB = 12$$ from condition 1).

Since $$AD + CD = 12$$ and $$AD = \frac{CD}{3}$$, we have $$\frac{CD}{3} + CD = 12, \frac{4CD}{3} = 12, 4CD = 36$$, or $$CD = 9$$. Then $$AD + 9 = 12$$, or $$AD = 3.$$

Then we have $$CE = 5 – AD, CE = 5 - 3$$, or $$CD = 2.$$

So, $$EB = 12 – CE, EB = 12 – 2,$$ or $$EB = 10.$$

Since both conditions yield a unique solution, they are 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 when the answer is A, B, C, or D.
_________________ Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS   [#permalink] 13 Oct 2019, 18:28

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