GMAT Math : Algebra

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Example Question #141 : Algebra

What is the value of $\dpi{100} \small 2x+2y$ ?

Statement 1: $\dpi{100} \small x-3y=4$

Statement 2: $\dpi{100} \small x+y=4$

Possible Answers:

EACH statement ALONE is sufficient.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient.

Statement 2 ALONE is sufficient, but statement 1 is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statements 1 and 2 TOGETHER are NOT sufficient.

Correct answer:

Statement 2 ALONE is sufficient, but statement 1 is not sufficient.

Explanation:

We know that we need 2 equations to solve for 2 variables, so it is tempting to say that both statements are needed. This is actually wrong! We aren't being asked for the individual values of x and y, instead we are being asked for the value of an expression.

$\dpi{100} \small 2x+2y$ is just $\dpi{100} \small 2\left ( x+y \right )$ , and statement 2 gives us the value of $\dpi{100} \small x+y$ . For data sufficiency questions, we don't actually have to solve the question, but if we wanted to, we would simply multiply statement 2 by 2.

$\dpi{100} \small 2x+2y=2\left ( x+y \right )=2$ * Statement 2 = $\dpi{100} \small 2\times 4=8$

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Example Question #142 : Algebra

Data Sufficiency Question- do not actually solve the problem

Solve for .

$\small 8vxy+9xz+10vyz=14$

1. $\small x=7$

2. $\small y=2$

Possible Answers:

Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

Both statements taken together are suffienct to answer the question, but neither statement alone is sufficient

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

Each statement alone is sufficient

Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Correct answer:

Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Explanation:

In order to solve an equation with 4 variables, you need to know either 3 of the variables or have a system of 4 equations to solve.

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Example Question #143 : Algebra

Solve for x,y,z .

Statement 1: 2x+4y-z=11

Statement 2: 5y+z=2

Possible Answers:

EACH statement ALONE is sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient.

Statement 2 ALONE is sufficient, but statement 1 is not sufficient.

Statements 1 and 2 TOGETHER are NOT sufficient.

Correct answer:

Statements 1 and 2 TOGETHER are NOT sufficient.

Explanation:

To solve for three unknowns, we need three equations. Therefore no combination of statements 1 and 2 will provide enough information to solve for $x,y,\ and\ z$ .

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Example Question #2 : Equations

Solve for $x,y,and\ z.$

Statement 1: 5x-3y+2z=1

Statement 2: 2y-5z=2,z=2

Possible Answers:

Statement 2 ALONE is sufficient, but statement 1 is not sufficient.

Statement 1 ALONE is sufficient, but statement 2 is not sufficient.

Statements 1 and 2 TOGETHER are NOT sufficient.

EACH statement ALONE is sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Correct answer:

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

To solve for three unknowns, we need three equations. Here we have three equations if we use both statements 1 and 2. We don't need to solve any further. Because this is a data sufficiency question, it doesn't matter what the actual values of x, y, and z are. The important fact is the we could find them if we wanted to.

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Example Question #941 : Data Sufficiency Questions

The volume of a fixed mass of gas varies inversely with the atmospheric pressure, in millibars, acting upon it, given that all other conditions remain constant.

At 12:00, a balloon was filled with exactly 100 cubic yards of helium. What is its current volume?

Statement 1: It is now 2:00.

Statement 2: The atmospheric pressure is now 105 millibars.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The first statement is unhelpful; the time of day is irrelevant to the question.

You can use the following variation equation to deduce the current volume:

$V_{1} P _{1} = V_{2} P _{2}$

or, equivalently,

$V_{2} = \frac{V_{1} P _{1} }{P _{2}}$

To find the current volume $V_{2}$ , you therefore need three things - the initial volume $V_{1}$ , which is given in the body of the question; the current pressure $P_{2}$ , which you know if you use Statement 2, and the initial pressure $P_{1}$ , which is not given anywhere.

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Example Question #6 : Dsq: Solving Equations

The electrical current through an object in amperes varies inversely as the object's resistance in ohms, given that all other conditions are equal.

Four batteries hooked up together run an electrical current of 3.2 amperes through John's flashlight. How much current would the same batteries run through John's radio?

Statement 1: The radio has resistance 20 ohms.

Statement 2: The flashlight has resistance 15 ohms.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Let $I_{1},R_{1}$ be the current through and the resistance of the flashlight; let $I_{2},R_{2}$ be the current through and the resistance of the radio.

The variation equation here would be:

$\frac{I_{1}}{R_{1}} = \frac{I_{2}}{R_{2}}$

or equivalently:

$\frac{I_{1}}{R_{1}} \cdot R_{2}= \frac{I_{2}}{R_{2}} \cdot R_{2}$

$I_{2} = \frac{I_{1}R_{2}}{R_{1}}$

So in order to find the current in the radio, you need to know three things - the current $I_{1}$ in the flashlight, which you know from the body of the problem; the resistance from the flashlight $R_{1}$ , which you know if you are given Statement 2; and the resistance from the radio $R_{2}$ , which you know if you are given Statement 1. Just substitute and solve.

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Example Question #942 : Data Sufficiency Questions

Evaluate:

$\log_{x} 100y - \log_{x} y$

Statement 1: x =10

Statement 2: y = 4

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

The difference of two logarithms with the same base is the same-base logarithm of the quotient of the numbers. Therefore, we can simplify this expression as

$\log_{x} 100y - \log_{x} y =\log_{x} \frac{100y}{y} = \log_{x} 100$

We need only know the value of , given to us in Statement 1, in order to evaluate this expression.

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Example Question #943 : Data Sufficiency Questions

is a positive integer

True or false?

(x - 2)(x-4)(x-6) = 0

Statement 1: x < 8

Statement 2: is even.

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

By the zero product principle, we can solve by setting each linear binomial to zero and solving. This yields three solutions:

$y - 2 = 0 \Rightarrow y = 2$

$y - 4 = 0 \Rightarrow y =4$

$y - 6= 0 \Rightarrow y = 6$

Neither statement alone narrows to one of these three solutions, but the two together do.

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Example Question #944 : Data Sufficiency Questions

Solve for :

$\left | 4x-3\right |-17=y^{2}-z^{2}$

(1) y-z=4

(2) y+z=12

Possible Answers:

Each statement ALONE is sufficient

Both statements TOGETHER are not sufficient

Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

Correct answer:

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

Explanation:

Solution

To solve for x, we need the value of $y^{2}-z^{2}$

$y^{2}-z^{2}=(y-z)(y+z)$

Therefore, we need both statements in order to solve for x.

$\left | 4x-3\right |-17= 4\times12$

$\left | 4x-3\right |-17=48$

$\left | 4x-3\right |=65$

4x-3=65 Or

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Example Question #945 : Data Sufficiency Questions

is a number not in the set $\left\{-1, 0, 1 \right\}$ .

Of the elements $\left \{ x, x^{2}, x^{3}\right \}$ , which is the greatest?

Statement 1: is a negative number.

Statement 2: $\left | x\right |>1$

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Explanation:

Assume Statement 1 alone. If is a negative number, then of the three given powers of in the set, only $x^{2}$ (the only even power) is positive. This makes $x^{2}$ the greatest of the three, thereby giving an answer to the question.

We show that Statement 2 alone is inconclusive by examining two values of whose absolute values are greater than 1 - namely, $\left \{-2, 2 \right \}$ .

Case 1: x = 2 . Then $x^{2}= 4$ and $x^{3} = 8$ , making $x^{3}$ the greatest number of the three.

Case 2: x = -2 . Then $x^{2}= 4$ and $x^{3} = -8$ , making $x^{2}$ the greatest number of the three.

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GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #141 : Algebra

Example Question #142 : Algebra

Example Question #143 : Algebra

Example Question #2 : Equations

Example Question #941 : Data Sufficiency Questions

Example Question #6 : Dsq: Solving Equations

Example Question #942 : Data Sufficiency Questions

Example Question #943 : Data Sufficiency Questions

Example Question #944 : Data Sufficiency Questions

Example Question #945 : Data Sufficiency Questions

All GMAT Math Resources

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