GMAT Math : Data-Sufficiency Questions

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Example Question #791 : Data Sufficiency Questions

Consider segment

I) Endpoint is located at the origin

II) has a distance of 36 units

Where is endpoint located?

Possible Answers:

Both statements are needed to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Correct answer:

Neither statement is sufficient to answer the question. More information is needed.

Explanation:

To find the endpoint of a segment, we can generally use the midpoint formula; however, in this case we do not have enough information.

I) Gives us one endpoint

II) Gives us the length of DF

The problem is that we don't know the orientation of DF. It could go in infinitely many directions, so we can't find the location of without more information.

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Example Question #791 : Data Sufficiency Questions

(2,3) is the midpoint of line PQ. What are the coordinates of point P?

(1) Point Q is the origin.

(2) Line PQ is 8 units long.

Possible Answers:

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

Statements (1) and (2) 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.

EACH statement ALONE is sufficient.

Correct answer:

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

Explanation:

The midpoint formula is

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$ ,

with statement 1, we know that Q is $\left ( 0,0\right )$ and can solve for P:

$\frac{0+x}{}2=2$ and $\frac{0+y}{}2=3$

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

x=4 y=6

$p=\left ( 4,6\right )$

Statement 1 alone is sufficient.

Statement 2 doesn't provide enough information to solve for point P.

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Example Question #1 : Midpoint Formula

A line segment has one of its endpoints at (12,13) . In which quadrant, or on what axis, is its other endpoint?

Statement 1: The midpoint of the segment is (9,9) .

Statement 2: The length of the segment is 10.

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:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 give us the means to find the other endpoint using the midpoint formula:

$x _{m } =\frac{x _{1 } + x _{2 }}{2}$

$9 =\frac{13 + x _{2 }}{2}$

$18 =12 + x _{2 }$

$x _{2 } = 6$

Similarly,

$y _{m } =\frac{y _{1 } + y _{2 }}{2}$

$9 =\frac{12 + y _{2 }}{2}$

$18 =13 + y _{2 }$

$y_{2 } = 5$

This makes the endpoint (6,5) , which is in Quadrant I.

Statement 2 is also sufficient. (12,13) , which is in Quadrant 1, is 12 units away from the nearest axis; since the length of the segment is 10, the entire segment must be in Quadrant I.

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Example Question #71 : Lines

In what quadrant or axis is the midpoint of the line segment with endpoints (A,B) and (B,A) located?

Statement 1: A > -B

Statement 2: (A,B) is in Quadrant IV.

Possible Answers:

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.

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 midpoint of the segment with endpoints (A,B) and (B,A) is $\left ( \frac{A+B}{2}, \frac{A+B}{2} \right )$ .

If A > -B , then A + B > 0 and $\frac{A+B}{2}>0$ , so the midpoint, having both of its coordinates positive, is in Quadrant I.

If (A,B) is in Quadrant IV, then A >0 and B <0 . But the quadrant of the midpoint varies according to and :

Example 1: If A = 8,B = -4 , the midpoint is $\left ( \frac{8+(-4) }{2}, \frac{8+(-4) }{2} \right )$ , or (2,2) , putting it in Quadrant I.

Example 2: If A = 4,B = -8 , the midpoint is $\left ( \frac{4-8 }{2}, \frac{4-8 }{2} \right )$ , or (-2,-2) , putting it in Quadrant III.

Therefore, the first statement, but not the second, tells us all we need to know.

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Example Question #2 : Midpoint Formula

Consider segment . What are the coordinates of the midpoint of ?

I) Point has coordinates of (3,6) .

II) Point has coordinates of (7,14) .

Possible Answers:

Each statement alone is enough to solve the question.

Statement 1 is sufficient to solve the question, but statement 2 is not sufficient to solve the question.

Neither statement is sufficient to solve the question. More information is needed.

Statement 2 is sufficient to solve the question, but statement 1 is not sufficient to solve the question.

Both statements taken together are sufficient to solve the question.

Correct answer:

Both statements taken together are sufficient to solve the question.

Explanation:

We are asked to find the midpoint of a line segment and given endpoints in our clues.

Midpoint formula is found by taking the average of the x and y values of two points.

$midpoint=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right )$

We need both endpoints to solve this problem, so both statements are needed.

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Example Question #4 : Dsq: Calculating The Midpoint Of A Line Segment

Find the midpoint of segment given that point is at (4,6) .

I) The coordinate of is twice that of , and the coordinate of is $\frac{3}{4}^{th}$ that of .

II) is $2\sqrt{5}$ units long.

Possible Answers:

Neither statement is sufficient to answer the question. More information is needed.

Either statement alone is sufficient to answer the question.

Both statements together are needed to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Correct answer:

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Explanation:

To find the midpoint, we need to know both endpoints.

I) Gives us the means to find out other endpoint.

II) Gives us the length of PS, but we are not given any hint as to its orientation.Thus, we cannot find the other endpoint and we cannot find the midpoint.

Thus, Statement I alone is sufficient to answer the question.

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Example Question #2901 : Gmat Quantitative Reasoning

Find the midpoint of segment .

I) Endpoint has coordinates of (76,148) .

II) Endpoint U's coordinate is half of I's , and U's coordinate is one sixteenth of I's coordinate.

Possible Answers:

Both statements are needed to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

To find the midpoint of a segment we need both endpoints

I) Gives us one endpoint.

II) Gives us clues to find the other endpoint.

has coordinates of (38,9.25)

Use midpoint formula

$(x_m,y_m)=\left(\frac{x_1-x_2}{2},\frac{y_1-y_2}{2}\right)$

$(x_m,y_m)=\left(\frac{76-38}{2},\frac{148-9.25}{2}\right)=(19,69.375)$

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Example Question #791 : Data Sufficiency Questions

Which is the greater quantity, $3^{x}$ or $9^{y}$ - or are they equal?

Statement 1: x = 2y + 2

Statement 2: x = 3y

Possible Answers:

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.

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.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 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:

From Statement 1 alone,

$3^{x} = 3^{2y+2} = 3^{2y} \cdot 3^{2} =\left ( 3^{2} \right ) ^{y}\cdot 9 = 9^{y} \cdot 9>9^{y}$

Now assume Statement 2 alone. We show that this is insufficient with two cases:

Case 1: x = 3,y= 1

$3^{3} = 27$ ; $9^{1} = 9$ ; therefore, $3^{x} >9^{y}$

Case 1: x = -3,y=- 1

$3^{-3} = \frac{1}{27}$ ; $9^{-1} = \frac{1}{9}$ ; therefore, $3^{x}<9^{y}$

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Example Question #2 : Algebra

Does $\log_{2} \left ( MN \right )$ exist?

Statement 1: and are both negative.

Statement 2: divided by 2 yields an integer.

Possible Answers:

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.

EITHER statement ALONE is 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:

A logarithm can be taken of a number if and only if the number is positive. If Statement 1 alone is true, then , being the product of two negative numbers, must be positive, and $\log_{2} \left ( MN \right )$ exists.

Statement 2 is irrelevant; 4 and both yield integers when divided by 2, but $\log_{2} 4 = 2$ and $\log_{2}\left ( -4 \right )$ does not exist.

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Example Question #1 : Algebra

Johnny was assigned to write a number in scientific notation by filling the circle and the square in the pattern below with two numbers.

$\bigcirc \times 10 ^{\square }$

Johnny filled in both shapes with numbers. Did he succeed?

Statement 1: He filled in the circle with the number "10".

Statement 2: He filled in the square with a negative integer.

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:

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

Explanation:

The number $a \times 10 ^{n}$ is a number written in scientific notation if and only of two conditions are true:

1) $1 \leq \left | a \right | < 10$

2) is an integer

By Statement 1 Johnny filled in the circle incorrectly, since it makes a = 10 .

By Statement 2, Johnny filled in the square correctly, but the statement says nothing about how he filled in the circle; Statement 2 leaves the question open.

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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 #791 : Data Sufficiency Questions

Example Question #791 : Data Sufficiency Questions

Example Question #1 : Midpoint Formula

Example Question #71 : Lines

Example Question #2 : Midpoint Formula

Example Question #4 : Dsq: Calculating The Midpoint Of A Line Segment

Example Question #2901 : Gmat Quantitative Reasoning

Example Question #791 : Data Sufficiency Questions

Example Question #2 : Algebra

Example Question #1 : Algebra

All GMAT Math Resources

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