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Math Expert V
Joined: 02 Sep 2009
Posts: 59633
If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 65% (01:54) correct 35% (02:07) wrong based on 331 sessions

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If x is an integer such that $$|2x + 1| < 3$$, then which of the following is a possible value of $$x^3 + 2x^2 + 5x + 10$$?

I. 0
II. 6
III. 10

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III

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Posts: 137
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Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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Bunuel wrote:
If x is an integer such that $$|2x + 1| < 3$$, then which of the following is a possible value of $$x^3 + 2x^2 + 5x + 10$$?

I. 0
II. 6
III. 10

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III

$$|2x + 1| < 3$$
$$-3 < 2x + 1 < 3$$
$$-2 < x < 1$$

$$x^3 + 2x^2 + 5x + 10$$ expression can be written as $$A=(x^2+5)(x+2)$$
So, in order to $$A$$ to be equal to $$0$$, $$x$$ must be $$-2$$ which is not possible.
When $$x=-1$$, $$A=6$$ and when $$x=0$$, $$A=10$$. Hence, $$II$$ and $$III$$ are possible values of $$A$$.

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Tulkin.
Target Test Prep Representative V
Status: Founder & CEO
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Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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Bunuel wrote:
If x is an integer such that $$|2x + 1| < 3$$, then which of the following is a possible value of $$x^3 + 2x^2 + 5x + 10$$?

I. 0
II. 6
III. 10

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III

We are given that x is an integer and that |2x + 1| < 3. We first solve for x by considering two cases:

Case 1: 2x + 1 < 3

2x < 2

x < 1.

Case 2: 2x + 1 > -3

2x > -4

x -2

Thus, we see that -2 < x < 1. The only integers that satisfy this inequality are 0 and -1.

If x = 0:

x^3 + 2x^2 + 5x + 10 = 10

If x = -1:

x^3 + 2x^2 + 5x + 10 = -1 + 2 - 5 + 10 = 6

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Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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1
Bunuel wrote:
If x is an integer such that $$|2x + 1| < 3$$, then which of the following is a possible value of $$x^3 + 2x^2 + 5x + 10$$?

I. 0
II. 6
III. 10

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III

Ans: D

Given : |2x+1|<3| ; means −3<2x+1<3 : further −2<x<1
because x an int and lies between -2 and 1 exclusive it can have only two values 0 and -1. by putting it in equation we get 10 and 6.
hence D is the ans.
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GMAT 1: 500 Q47 V15 GPA: 3.4
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Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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Bunuel wrote:
If x is an integer such that $$|2x + 1| < 3$$, then which of the following is a possible value of $$x^3 + 2x^2 + 5x + 10$$?

I. 0
II. 6
III. 10

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III

Solution :-

We need to follow below example:-
|x| = 2. Then we always write -2 < x < 2. That is value of x ranges from -2 to 2.

Similarly,
|2x+1|<3 can be written as
−3<2x+1<3
−3-1<2x<3-1
-4<2x<2
-2<x<1.

Possible values of x is -1 and 0.
Substitute in the expression given to get the answer.
$$x^3 + 2x^2 + 5x + 10$$.

Let's put x = -1
$$(-1)^3 + 2(-1)^2 + 5(-1) + 10$$ = -1+2-5+10 = 12-6 = 6.

Let's put x =0. Clearly expression gives output as 10.

So, 6 & 10 is right ans.

Ans D
Intern  B
Joined: 27 Jun 2017
Posts: 3
Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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|2x+1|<3
which means -4<2x<2
-2<x<1
so x can take two values : -1 and 0
apply each value of x to x^3+2x^2+5x+10
for 0 we will get 10
for -1 we will get 6
so option D is the right answer
Manager  B
Joined: 31 Jan 2018
Posts: 67
GMAT 1: 700 Q46 V40 Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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Bunuel wrote:
If x is an integer such that $$|2x + 1| < 3$$, then which of the following is a possible value of $$x^3 + 2x^2 + 5x + 10$$?

I. 0
II. 6
III. 10

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III

The give inequality is |2x + 1| <3
==>-3<2x + 1<3
==> -3-1<2x<3-1
==> -4<2x<2
==> -2<x<1
Since the x is an integer, the value of x will be -1 and 0
And for x = -1 the value of the expression is 6
for x = 0 the value of the expression is 11

Hence the answer will be (D)
Intern  B
Joined: 28 Sep 2017
Posts: 4
Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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ScottTargetTestPrep wrote:
Bunuel wrote:
If x is an integer such that $$|2x + 1| < 3$$, then which of the following is a possible value of $$x^3 + 2x^2 + 5x + 10$$?

I. 0
II. 6
III. 10

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, III

We are given that x is an integer and that |2x + 1| < 3. We first solve for x by considering two cases:

Case 1: 2x + 1 < 3

2x < 2

x < 1.

Case 2: 2x + 1 > -3

2x > -4

x -2

Thus, we see that -2 < x < 1. The only integers that satisfy this inequality are 0 and -1.

If x = 0:

x^3 + 2x^2 + 5x + 10 = 10

If x = -1:

x^3 + 2x^2 + 5x + 10 = -1 + 2 - 5 + 10 = 6

Hello, i was solving another problem - If |x^2 − 12| = x, which of the following could be the value of x? : Problem Solving (PS)

You provided a solution on this question and explained that value of |x^2-12| will be +ve. Then how | 2x-1| can have + and - value.

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Location: India
Schools: ISB '21 (WL)
GMAT 1: 710 Q48 V38 Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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x>-2 and x<1. Therefore, x = 0 or x = 1, as x is an integer.
Replacing x in equation, hence, value = 6 or value = 10

D

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Re: If x is an integer such that |2x + 1| < 3, then which of the following  [#permalink]

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_________________ Re: If x is an integer such that |2x + 1| < 3, then which of the following   [#permalink] 07 Jul 2019, 12:58
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