GMAT Math : x and y intercept

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Example Question #11 :Dsq: Calculating X Or Y Intercept

曼迪的老师要求她写数字the circle, the square, and the triangle in the pattern below in order to make an equation whose graph has-intercept (5,0) and-intercept (0, 1) .

$\square x+ \bigcirc y = \triangle$

Did Mandy succeed?

Statement 1: Mandy wrote a 5 in the triangle.

Statement 2: The number Mandy wrote in the square was five times the number she wrote in the circle.

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

Explanation:

Let A,B,C stand for the values Mandy wrote in the square, the circle, and the triangle, respectively. The equation becomes

A x+ B y =C .

From Statement 1 alone, we know that Mandy wrote a 5 in the triangle, but we do not know any of the others. The question of Mandy's success is unresolved.

Now assume Statement 2 alone is known. Then

A = 5B .

The equation can be rewritten as

5B x+ B y =C

and it can be rewritten in slope-intercept form as

B y =-5B x+C

$\frac{B y}{B} =\frac{-5B x+C}{B}$

$y= -5x + \frac{C}{B}$

Mandy wrote an equation whose line has slope.

However, the slope of a line through (5,0) and (0, 1) is

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{1-0}{0-5} = \frac{1}{-5}= -\frac{1}{5}$ .

Statement 2 alone is sufficient to establish that Mandy did not succeed.

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Example Question #12 :Dsq: Calculating X Or Y Intercept

一个line on the coordinate plane is neither horizontal nor vertical. Give its-intercept.

Statement 1: The line has slope $\frac{1}{4}$ .

Statement 1: The line passes through the origin.

Possible Answers:

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

BOTH statements TOGETHER are insufficient 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 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

Statement 1 provides insufficient information, since the slope of the line alone is not enough from which to deduce the-intercept. Statement 2 alone tells us that the line passes through the point (0,0) ; since this is on the-axis, this is the-intercept.

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例子问题# 13:Dsq: Calculating X Or Y Intercept

Stanley's teacher challenged him to write numbers in the circle, the square, and the triangle in the pattern below in order to make an equation whose graph has-intercept (4,0) .

$\square x+ \bigcirc y = \triangle$

Did Stanley succeed?

Statement 1: Stanley wrote a 4 in the square.

Statement 2: Stanley wrote a 16 in the triangle.

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.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient 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 A,B,C stand for the values Stanley wrote in the square, the circle, and the triangle, respectively. The equation becomes

A x+ B y =C .

To find the-coordinate of the-intercept, set y = 0 and solve for:

$Ax+ B \cdot 0 =C$

Ax=C

$x=\frac{C}{A}$

It is therefore necessary and sufficient to know the values ofand- the values Ralph wrote in the square and the triangle - in order to determine the-intercept of Ralph's equation. Each statement alone give only one of those numbers; the two together give both.

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Example Question #14 :Dsq: Calculating X Or Y Intercept

一个function f(x) is graphed on the coordinate plane. It has exactly one-intercept. What is it?

Statement 1: f(5)= 0

Statement 2: f(0)= 7

Possible Answers:

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 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.

Correct answer:

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

Explanation:

The-intercept of the graph ofis the point at which it intersects the-axis. Since this point has-coordinate 0, the-coordinate is the value for which f(x)= 0 . Statement 1 gives us this value; Statement 2 does not.

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Example Question #15 :Dsq: Calculating X Or Y Intercept

Continuous function g(x) has the set of all real numbers as its domain.

How many-intercepts does the graph g(x) have?

Statement 1: If M<N , then g(M)<g(N) .

Statement 2: g(0)= 0 .

Possible Answers:

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

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:

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

Explanation:

Statement 1 alone establishes thatis always increasing. Its graph cannot have more than one-intercept; if it does, then the graph of the function must have a vertex between two intercepts, violating this statement. But it does not answer the question as to how many interceptshas, as seen in these two cases:

Case 1:

g(x) = x+1

This is a linear function that is always increasing—it is in slope-intercept form, and its slope is 1, a positive number. The graph ofhas exactly one-intercept.

Case 2:

$g(x)=2^{x}$

一个n exponential function with a base greater than 1, such as this, is an increasing function; however, 2 raised to any power must be positive, so there is no valuefor which g(N)= 0 . The graph ofhas no-intercepts.

Statement 2 alone establishes that at least one-intercept exists - since g(0)= 0 , (0,0) is an-intercept. It does not, however, rule out the possibility of more-intercepts.

Now assume both statements are true. Since Statement 1 establishes that there is at most one-intercept, and Statement establishes that there is at least one-intercept, the two statements together establish that there is exactly one.

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Example Question #16 :Dsq: Calculating X Or Y Intercept

Ray's teacher challenged him to write numbers in the circle and the square in the pattern below in order to make an equation whose graph has-intercept (0, 5) .

$y = \square x+ \bigcirc$

Did Ray succeed?

Statement 1: Ray wrote a 5 in the square.

Statement 2: Ray wrote a 7 in the circle.

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.

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 insufficient to answer the question.

Correct answer:

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

Explanation:

If we letstand for the number Ray wrote in the square andstand for the number he wrote in the circle, the equation becomes

y = mx+b ,

the slope-intercept form of the equation of a line. In this form, the-intercept is solely determined by the value of—namely, the value that Ray wrote in the circle. Statement 1 is therefore irrelevant, and Statement 2 alone establishes that Ray did not succeed.

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Example Question #17 :Dsq: Calculating X Or Y Intercept

Continuous function g(x) has the set of all real numbers as its domain.

How many-intercepts does the graph g(x) have?

Statement 1: If 0<M<N , then g(M)<g(N) .

Statement 2: If M<N < 0 , then g(M)>g(N) .

Possible Answers:

BOTH statements TOGETHER are insufficient 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.

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:

一个ssume both statements are true.

By Statement 1,is decreasing on the domain interval $\left ( -\infty, 0\right )$ ; by Statement 2,is increasing on the domain interval $(0, \infty)$ . Therefore,must have its minimum value when x= 0 .

This does not, however, tell us the number of-intercepts. For example, the graph of $g(x)=x^{2}$ has as its minimum point (0,0) , and, subsequently, exactly one-intercept. The graph of $g(x)=x^{2} + 1$ has as its minimum point (0,1) and, subsequently, no-intercepts.

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Example Question #18 :Dsq: Calculating X Or Y Intercept

Ralph's teacher challenged him to write numbers in the circle, the square, and the triangle in the pattern below in order to make an equation whose graph has-intercept (0, 4) .

$\square x+ \bigcirc y = \triangle$

Did Ralph succeed?

Statement 1: Ralph wrote a在短时are.

Statement 2: Ralph wrote ain the triangle.

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 insufficient to answer the question.

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

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Let A,B,C stand for the values Ralph wrote in the square, the circle, and the triangle, respectively. The equation becomes

A x+ B y =C .

To find the-coordinate of the-intercept, set x = 0 and solve for:

$A \cdot 0 + B y =C$

B y =C

$y =\frac{C}{B}$

It is therefore necessary and sufficient to know the values ofand- the values Ralph wrote in the circle and the triangle - in order to determine the-intercept of Ralph's equation. Statement 1 is irrelevant, and Statement 2 only provides the value Ralph wrote in the triangle.

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Example Question #19 :Dsq: Calculating X Or Y Intercept

Gloria's teacher challenged her to write numbers in the circle and the square in the pattern below in order to make an equation whose graph has-intercept (6,0) .

$y = \square x+ \bigcirc$

Did Gloria succeed?

Statement 1: Gloria wrote a在短时are.

Statement 2: Gloria wrote ain the circle.

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.

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 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:

If we letstand for the number Gloria wrote in the square andstand for the number she wrote in the circle, the equation becomes

y = mx+b ,

the slope-intercept form of the equation of a line. We can find the-coordinate of the-intercept by setting y = 0 and solving for:

mx+b = 0

mx+b - b= 0 - b

mx = -b

$\frac{mx }{m}= \frac{-b}{m}$

$x = -\frac{b}{m}$

Therefore, it is necessary and sufficient to know bothand- both of the numbers Gloria wrote - to determine the-intercept of the equation she made. Neither statement provides both values, but both statements together do.

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Example Question #1 :Dsq: Calculating The Equation Of A Curve

In the-plane, the equation of lineis

ax+by+c=0 $\left ( abc\neq 0 \right )$ .

The slope of lineis 2. What is the value of?

(1) a+b=4

(2) c=-3

Possible Answers:

EACH statement ALONE is sufficient.

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.

Correct answer:

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

Explanation:

The slope of lineis $-\frac{a}{b}=2$

From statement (1) we get another function ofand. Therefore, we can calculate the values ofand.

From $-\frac{a}{b}=2$

we can get a=-2b .

Plug a=-2b into a+b=4 , then we can get

b=-4

and

$a=-2\cdot -4=8$

Statement (2) only tells us the value of, which is useless to get the value of, because we have three unknown numbers with only two equations given.

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GMAT Math : x and y intercept

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #11 :Dsq: Calculating X Or Y Intercept

Example Question #12 :Dsq: Calculating X Or Y Intercept

例子问题# 13:Dsq: Calculating X Or Y Intercept

Example Question #14 :Dsq: Calculating X Or Y Intercept

Example Question #15 :Dsq: Calculating X Or Y Intercept

Example Question #16 :Dsq: Calculating X Or Y Intercept

Example Question #17 :Dsq: Calculating X Or Y Intercept

Example Question #18 :Dsq: Calculating X Or Y Intercept

Example Question #19 :Dsq: Calculating X Or Y Intercept

Example Question #1 :Dsq: Calculating The Equation Of A Curve

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