If x is an integer such that |2x + 1|

Question

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

Tulkin987 · Answer

|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 .

Answer: D

D3N0 · Answer

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.

rjkmr · Answer

|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

ScottTargetTestPrep · Answer

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 Answer: D

zishu912 · Answer

The give inequality is |2x + 1| <3 ==>-3<2x + 1<3 ==> -3-1<2x<3-1 ==> -4<2x<2 ==> -2

AvinashT2303 · Answer

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.

Posted from my mobile device

thinkTheta · Answer

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

Sent from my iPhone using  GMAT Club Forum mobile app

SSM700plus · Answer

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

bumpbot · Answer

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If x is an integer such that |2x + 1| < 3, then which of the following

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