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# If a^2 -10 < 1590, then how many integer values can a have

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Current Student
Joined: 28 May 2014
Posts: 515
GMAT 1: 730 Q49 V41
If a^2 -10 < 1590, then how many integer values can a have  [#permalink]

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04 Apr 2017, 04:48
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Difficulty:

45% (medium)

Question Stats:

55% (01:14) correct 45% (01:28) wrong based on 172 sessions

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If a^2 -10 < 1590, then how many integer values can a have?

(A) 78
(B) 79
(C) 80
(D) 81
(E) 101

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Math Expert
Joined: 02 Sep 2009
Posts: 58353
Re: If a^2 -10 < 1590, then how many integer values can a have  [#permalink]

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04 Apr 2017, 04:52
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saswata4s wrote:
If a^2 -10 < 1590, then how many integer values can a have?

(A) 78
(B) 79
(C) 80
(D) 81
(E) 101

a^2 -10 < 1590

a^2 < 1600

-40 < a < 40.

a can take 79 integer values: 39 negative, 0 and 39 positive.

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Target Test Prep Representative
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Re: If a^2 -10 < 1590, then how many integer values can a have  [#permalink]

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21 May 2018, 16:39
saswata4s wrote:
If a^2 -10 < 1590, then how many integer values can a have?

(A) 78
(B) 79
(C) 80
(D) 81
(E) 101

Simplifying the inequality, we have:

a^2 < 1600

a < 40

Or

-a < 40

a > -40

So we have:

-40 < a < 40

So there are 79 integer values for a. This includes the 39 possible positive values for a (1 to 39, inclusive), the 39 possible negative values for a (-1 to -39, inclusive), and 0, making a total of 79.

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Re: If a^2 -10 < 1590, then how many integer values can a have  [#permalink]

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21 May 2018, 18:44
If a^2 -10 < 1590, then how many integer values can a have?

$$a^2$$-10 < 1590. , if a = 40 , then $$a^2$$ = 1600.

Critical Information:
1. We should not forget to consider negative integers
2. 0 is also included in integers.

-39 < a < 39.

A can take values from: 39 negative integers (-1 to -39) , 0 , 39 positive integers (1 to 39) = 79 Integers

Ans:B
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Re: If a^2 -10 < 1590, then how many integer values can a have  [#permalink]

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21 May 2018, 19:00
saswata4s wrote:
If a^2 -10 < 1590, then how many integer values can a have?

(A) 78
(B) 79
(C) 80
(D) 81
(E) 101

$$a^2 -10 < 1590$$

$$a^2 < 1590 + 10$$

$$a^2 < 1600$$

a can take values from -39 to 39. because -40 < a < 40.

A can take values from: 39 negative integers (-1 to -39) , 0 , 39 positive integers (1 to 39).

No of values that a can take - 39 + 39 +1 = 79.

Ans - B
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Sudhanshu
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Re: If a^2 -10 < 1590, then how many integer values can a have  [#permalink]

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12 Apr 2019, 17:57
Hello JeffTargetTestPrep

Just one question,

Why is not like the following?

$$a^2 -10 < 1590$$

$$a^2 < 1600$$

$$a < (+/-) 40$$ so... $$a < 40$$ and $$a < - 40$$

Kind regards!
Re: If a^2 -10 < 1590, then how many integer values can a have   [#permalink] 12 Apr 2019, 17:57
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