GMAT Math : Data-Sufficiency Questions

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Example Questions

Example Question #931 : Data Sufficiency Questions

What is if, $\left | x-4\right |=6$ ?

(1) x=A

(2) $\left | A\right |=10$

Possible Answers:

Each statement alone is sufficient.

Statements 1 and 2 together are not sufficient.

Both statements together are sufficient.

Statement 1 alone is sufficient.

Statement 2 alone is sufficient.

Correct answer:

Both statements together are sufficient.

Explanation:

To begin with this problem, we should try to solve $\left | x-4\right |=6$ . It gives us two sets of equations for us to find values for ; x-4=6 and x-4=-6 . Solving gives us two possible values for , and . Let's see how can the statements help us determine the value of .

Statement 1 gives us an other unknown for the value of . Therefore, this statement is insufficient.

Statement 2 gives an absolute value for this unknown . But we don't know what other values is equal to.

Taken together these statements, allow us to see that must be and therefore are sufficient to answer the question.

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Example Question #11 : Dsq: Solving Linear Equations With One Unknown

$\left | x-8\right |=A$ . What is ?

(1) A=0

(2) A=x-8

Possible Answers:

Each statement alone is sufficient.

Statement 2 alone is sufficient.

Statement 1 alone is sufficient.

Both statements together are sufficient.

Statements 1 and 2 together are not sufficient.

Correct answer:

Each statement alone is sufficient.

Explanation:

To approach this problem, we should firstly set up two possible equations for the value of ; either x-8=A or x-8=-A .

Statement 1 tells us that is in fact zero. Than the equations return a single value for , therefore statement 1 alone is sufficient.

Statement 2 tells us that A=x-8 , if plug in this value for , we get that:

|x-8|=x-8

Because there is the absolute value we get two equations:

x-8=x-8

x=x+0

0=0

x-8=-(x-8)

x-8=-x+8

2x=16

x=8

must be 8. Plugging in the value for in our first equation gives us no solution because both sides are of equal value and we end up with 0=0 .

Therefore, statement 2 alone is sufficient

To conclude, each statement alone is sufficient.

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Example Question #933 : Data Sufficiency Questions

What is ?

(1) $x^{2}=9$

(2) $\left | x^{3} \right |=27$

Possible Answers:

Statements 1 and 2 taken together are not sufficient.

Statement 2 alone is sufficient.

Each statement alone is suffcient.

Both statements together are sufficient.

Statement 1 alone is sufficient.

Correct answer:

Statements 1 and 2 taken together are not sufficient.

Explanation:

To answer this question, we must find a single value for .

Statement 1 gives us an equation with two possible solutions for . Therefore, statement 1 alone is not sufficient, since can either be or

Statemnt 2 alone is also insufficient, because it gives us the same possible values for as the equation in statement 1.

When two statements give us the same the information the answer is either both statements together are sufficient or statements 1 and 2 together are not sufficient. Here neither statement allowed us to answer, it follows that statements 1 and 2 together are not sufficient.

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Example Question #131 : Algebra

x=A , What is ?

(1) A+B= 3

(2) A-B=1

Possible Answers:

Statements 1 and 2 together are not sufficient.

Both statements together are sufficient.

Each statement alone is sufficient.

Statement 1 alone is sufficient.

Statement 2 alone is sufficient.

Correct answer:

Both statements together are sufficient.

Explanation:

To find a value for , we should be able to get a value for .

Statement 1 has two unknowns therefore we need another different equation with A,B to be able to find values for these unknowns.

Statement 2 alone is also insufficient because just as statement 1 has two variables and therefore we need more information to solve it.

Taking together these equations, by adding both sides we get 2A=4 and from there we can find a single value for .

Both statements together are sufficient.

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Example Question #931 : Data Sufficiency Questions

$\left |\frac{1}{x-1} \right |=3$ and is different than . What is ?

(1) x>1

(2) is not an integer.

Possible Answers:

Statements 1 and 2 together are sufficient.

Each statement alone is sufficient.

Both statements together are sufficient.

Statement 1 alone is sufficient.

Statement 2 alone is sufficient.

Correct answer:

Statement 1 alone is sufficient.

Explanation:

Firstly we should try to see what are the possible values for , by solving the equations given by the absolute value:

either $\frac{1}{x-1}=3$ or $\frac{1}{x-1}=-3$ .

This allows us to find two values for which are $\frac{2}{3}$ and $\frac{4}{3}$ , let's see how the statements can help us determine a single value for .

Statement 1 tells us that must be greater than one. Only one of our solutions for is greater than one. Therefore, statement 1 alone is sufficient.

Statement 2 tells us that is not an integer, however both solutions are not integer values and therefore statement 2 doesn't help us find a single solution.

Statement 1 alone is sufficient.

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Example Question #1 : Dsq: Solving Equations

If $\dpi{100} \small z+x=y$ , what is the value of $\dpi{100} \small x$ ?

(1) $\dpi{100} \small z=7$

(2) $\dpi{100} \small y+7=z$

Possible Answers:

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

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

EACH statement ALONE is sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Correct answer:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Explanation:

$\dpi{100} \small z+x=y$

Therefore, $\dpi{100} \small x=y-z$

(1) If $\dpi{100} \small z=7$ , then $\dpi{100} \small y-z=y-7$ , and the value of $\dpi{100} \small y-7$ can vary. $\dpi{100} \small \rightarrow$ NOT sufficient

(2) Subtracting both $\dpi{100} \small z$ and 7 from each side of $\dpi{100} \small y+7=z$ gives $\dpi{100} \small y-z=-7$ .

The value of $\dpi{100} \small y-z$ can be determined. $\dpi{100} \small \rightarrow$ SUFFICIENT

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Example Question #2 : Dsq: Solving Equations

If $\dpi{100} \small x> 0$ , what is the value of x?

Statement 1: $\dpi{100} \small x> 1$

Statement 2: $\dpi{100} \small x^{2}-4=0$

Possible Answers:

Statements 1 and 2 TOGETHER are NOT sufficient.

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

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

EACH statement ALONE is sufficient.

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

Correct answer:

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

Explanation:

We are looking for one value of x since the quesiton specifies we only want a positive solution.

Statement 1 isn't sufficient because there are an infinite number of integers greater than 1.

Statement 2 tells us that x = 2 or x = –2, and we know that we only want the positive answer. Then Statement 2 is sufficient.

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Example Question #3 : Dsq: Solving Equations

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:

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

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

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 #3051 : Gmat Quantitative Reasoning

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

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

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

Each statement alone is sufficient

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

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 #5 : Dsq: Solving Equations

Solve for x,y,z .

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

Statement 2: 5y+z=2

Possible Answers:

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.

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

EACH statement ALONE is 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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GMAT Math : Data-Sufficiency Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #931 : Data Sufficiency Questions

Example Question #11 : Dsq: Solving Linear Equations With One Unknown

Example Question #933 : Data Sufficiency Questions

Example Question #131 : Algebra

Example Question #931 : Data Sufficiency Questions

Example Question #1 : Dsq: Solving Equations

Example Question #2 : Dsq: Solving Equations

Example Question #3 : Dsq: Solving Equations

Example Question #3051 : Gmat Quantitative Reasoning

Example Question #5 : Dsq: Solving Equations

All GMAT Math Resources

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