The sequence S consists of 10 terms: x, x2, x3x10, where x is a non-zero number. If P is the sum of all the terms in the sequence S, is P3 0?(1) The distance of any term of the sequence S from zero on the number line is not less than 1.(2) x5 = x7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?

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The sequence S consists of 10 terms: x, x², x³……x¹⁰, where x is a non-zero number. If P is the sum of all the terms in the sequence S, is P3

> 0?

(1) The distance of any term of the sequence S from zero on the number line is not less than 1.

(2) x⁵ = x⁷

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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

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The sequence S consists of 10 terms: x, x2, x3……x10, where...

Steps 1 & 2: Understand Question and Draw Inferences

Sequence S= {x,x²,x³,…….x¹⁰}

P = x+x²+x³+…….+x¹⁰

To Find: Is P³> 0 ?

P³> 0. If P > 0 (Since P is raised to an odd power that does not affects its sign)

As P = x+x²+x³……….+x¹⁰ , the positive or negative nature of P will depend on the positive or negative nature of x. Hence, following cases can arise:

If x > 0 → In this case, x,x²,x³,…….x¹⁰ > 0. So, their sum will also be positive. Hence P > 0

If x < 0 → The terms with an odd power i.e. x,x²,x³,…….x⁹ < 0 and the terms with an even power i.e. x,x²,x³,…….x¹⁰ > 0. So, the value of P will depend on the sum of the terms with an odd power and the terms with an even power. Also we know that if -1 < x < 0, with increasing power the magnitude of the terms decrease ( |x| > |x²|, while if x < -1, the magnitude of the terms increase with increasing power(|x| < |x²|). So, the following cases are possible:

- To understand the nature of P, let’s evaluate the first term of P in the equation above i.e.x + x². Here x < 0 and x² > 0. Since the magnitude of x is less than 1, the magnitude of x² will be less than x. For ex: if x = -0.5, x² = 0.25. Hence x + x² < 0. Similarly x³ + x⁴ < 0. So, we see here that P is the sum of 5 negative numbers. Hence P < 0.
- To understand the nature of P, let’s evaluate the first term of P in the equation above i.e. x + x². Here x < -1 and x² > 0. Since the magnitude of x is greater than 1, the magnitude of x² will be greater than x. For ex: if x = -2, x² = 4. Hence x + x² > 0. Similarly x³ + x⁴ > 0. So, we see here that P is the sum of 5 positive numbers. Hence P > 0.
However there may be a case where the terms
- This would be possible when x(x+1) = 0, i.e. x = 0 or -1. As x≠ 0, for x = -1, P = 0.

So, P > 0, except when -1 < x < 0. Hence, we need to find if -1 < x < 0.

Step 3: Analyze Statement 1 independently

(1) The distance of any term of the sequence S from zero on the number line is not less than 1.

As the distance of all the terms of the sequence from zero is not less than 1, the distance of the first term i.e. |x| ≥ 1. If |x| ≥ 1, ∣∣x²∣∣≥1………………….∣∣x¹⁰∣∣≥1

So, x ≥ 1 or x ≤ -1. Following cases can arise:

So, we cannot say for sure if P > 0 or not. Insufficient to answer.

Step 4: Analyze Statement 2 independently

If x = -1, P = 0
x ≠ 0(given in the question statement)
If x = 1, P > 0

So, we cannot say for sure if P > 0. Insufficient to answer

Step 5: Analyze Both Statements Together (if needed)

x ≥ 1 or ≤ -1
x = -1 or 1

Combining both the statements, we have x = -1 or 1.

If x = -1, P = 0
If x = 1, P > 0

So, we cannot say for sure if P > 0.

Insufficient to answer.

Answer: E

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The sequence S consists of 10 terms: x, x2, x3……x10, where x is a non-zero number. If P is the sum of all the terms in the sequence S, is P3> 0?(1) The distance of any term of the sequence S from zero on the number line is not less than 1.(2) x5 = x7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?

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The sequence S consists of 10 terms: x, x2, x3……x10, where x is a non-zero number. If P is the sum of all the terms in the sequence S, is P3> 0?(1) The distance of any term of the sequence S from zero on the number line is not less than 1.(2) x5 = x7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. 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 The sequence S consists of 10 terms: x, x2, x3……x10, where x is a non-zero number. If P is the sum of all the terms in the sequence S, is P3> 0?(1) The distance of any term of the sequence S from zero on the number line is not less than 1.(2) x5 = x7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sequence S consists of 10 terms: x, x2, x3……x10, where x is a non-zero number. If P is the sum of all the terms in the sequence S, is P3> 0?(1) The distance of any term of the sequence S from zero on the number line is not less than 1.(2) x5 = x7a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'E'. Can you explain this answer?.

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