In the xy-plane, is the x-intercept of the line y = mx + b positive? (m and b are non-zero numbers)(1) The y-intercept of the line m2y = bx + m is positive.(2) The x-intercept of the line is positivea)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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GMAT Exam > GMAT Questions > In the xy-plane, is the x-intercept of the li...

In the xy-plane, is the x-intercept of the line y = mx + b positive? (m and b are non-zero numbers)

(1) The y-intercept of the line m²y = bx + m is positive.

(2) The x-intercept of the line

is positive

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'C'. Can you explain this answer?

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In the xy-plane, is the x-intercept of the line y = mx + b positive? (...

Steps 1 & 2: Understand Question and Draw Inferences

Let’s find the x-intercept of the given line.

When the line intercepts the x-axis, the y-coordinate becomes 0.

Substituting y = 0 in the given equation of the line,

The question thus becomes

Multiplying by -1 on both sides of the inequality, the question modifies to

Step 3: Analyze Statement 1

To compare the given line with the general form of the equation (y= mx + c), we divide both sides of the equation with m².

The equation becomes y

we see that the y-intercept of the given line m²y = bx + m is 1/m

The statement tells us that 1/m>0

Using this information, we can only say that m > 0.

However, b/m can be negative or not depending on whether b is negative or not.

INSUFFICIENT.

Step 4: Analyze Statement 2

In order to find the x-intercept of the given equation of line my = x + m, we substitute y = 0 in the given equation to get

Since

only when b < 0.

Is b/m < 0 ? We cannot be sure because we only know that b < 0. b/m

can be less than 0 or not depending on whether m is positive or not.

Step 5: Analyze Both Statements Together (if needed)

Combining statements (1) and (2),

we have m > 0 and b < 0.

This means that b/m < 0 for all such values of m and b.

SUFFICIENT.

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In the xy-plane, is the x-intercept of the line y = mx + b positive? (m and b are non-zero numbers)(1) The y-intercept of the line m2y = bx + m is positive.(2) The x-intercept of the line is positivea)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?

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In the xy-plane, is the x-intercept of the line y = mx + b positive? (m and b are non-zero numbers)(1) The y-intercept of the line m2y = bx + m is positive.(2) The x-intercept of the line is positivea)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the xy-plane, is the x-intercept of the line y = mx + b positive? (m and b are non-zero numbers)(1) The y-intercept of the line m2y = bx + m is positive.(2) The x-intercept of the line is positivea)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the xy-plane, is the x-intercept of the line y = mx + b positive? (m and b are non-zero numbers)(1) The y-intercept of the line m2y = bx + m is positive.(2) The x-intercept of the line is positivea)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'C'. Can you explain this answer?.

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