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# The integers A, B, and C are consecutive and A < B < C. If A^2 = C

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Math Expert
Joined: 02 Sep 2009
Posts: 42278

Kudos [?]: 132880 [0], given: 12390

The integers A, B, and C are consecutive and A < B < C. If A^2 = C [#permalink]

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13 Oct 2017, 00:05
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Difficulty:

25% (medium)

Question Stats:

77% (00:30) correct 23% (01:04) wrong based on 47 sessions

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The integers A, B, and C are consecutive and A < B < C. If A^2 = C, which of the following could be the value of A?

I. –1
II. 0
III. 2

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132880 [0], given: 12390

Intern
Joined: 29 Aug 2017
Posts: 35

Kudos [?]: 2 [0], given: 48

Re: The integers A, B, and C are consecutive and A < B < C. If A^2 = C [#permalink]

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13 Oct 2017, 05:06
Bunuel wrote:
The integers A, B, and C are consecutive and A < B < C. If A^2 = C, which of the following could be the value of A?

I. –1
II. 0
III. 2

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

$$A+2 = A^2$$
$$A^2 - A - 2 = 0$$
$$(A-2)(A+1) = 0$$
$$A = 2$$ $$or -1$$

Answer is D.

Kudos [?]: 2 [0], given: 48

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 906 [0], given: 5

Re: The integers A, B, and C are consecutive and A < B < C. If A^2 = C [#permalink]

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16 Oct 2017, 17:08
Bunuel wrote:
The integers A, B, and C are consecutive and A < B < C. If A^2 = C, which of the following could be the value of A?

I. –1
II. 0
III. 2

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

Let’s test out Roman numerals to see if we have A^2 = C.

I. If A = -1, then B = 0 and C = 1. Since (-1)^2 = 1, Roman numeral I works.

II. If A = 0, then B = 1 and C = 2. Since 0^2 = 0 ≠ 2, Roman numeral II does not work.

III. If A = 2, then B = 3 and C = 4. Since 2^2 = 4, Roman numeral III works.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
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Kudos [?]: 906 [0], given: 5

Re: The integers A, B, and C are consecutive and A < B < C. If A^2 = C   [#permalink] 16 Oct 2017, 17:08
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# The integers A, B, and C are consecutive and A < B < C. If A^2 = C

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