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Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5

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pranavpal
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   06 Apr 2018, 21:34
ydmuley wrote:
Is x<5 ?

\((2) x^2 + x < 5\)

\(x^2 + x < 5\)

\(x(x + 1) < 5\)

\(x < 5\) or

\(x < 4\)

As both these values are < 5

(2) =====> is SUFFICIENT

Hence, Answer is B


can anyone please solve the second statement in detail ?
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Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   11 Apr 2019, 23:32
Hi Bunuel VeritasKarishma,

I need ur expert opinion in this..

I got the answer correct but need to know whether my process is correct or no..

S2: x^2+x<5
X^2+x-5<0
(X+1)(x-5)<0

X<-1 or x<5

Posted from my mobile device
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   11 Apr 2019, 23:48
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Shef08 wrote:
Hi Bunuel VeritasKarishma,

I need ur expert opinion in this..

I got the answer correct but need to know whether my process is correct or no..

S2: x^2+x<5
X^2+x-5<0
(X+1)(x-5)<0

X<-1 or x<5

Posted from my mobile device


(x + 1)*(x - 5) is not the same as (x^2 + x - 5). It is same as (x^2 - 4x -5).

(x^2 + x - 5) does not have integer roots but we can guess the roots using the formula as done in this comment above: https://gmatclub.com/forum/is-x-5-1-x-2 ... l#p2042359

If the roots are approximately -3 and 2, then (x^2 + x - 5) = (x + 3)(x - 2) < 0
which gives us -3 < x < 2
So in any case, x is less than 5.
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Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   03 Sep 2020, 06:41
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Is x<5 ?

Statement Two Alone:

x^2 + x < 5

Thus, we have x < 5 - x^2. Since x^2 is nonnegative, we have 5 - x^2 ≤ 5. Since x < 5 - x^2 and 5 - x^2 ≤ 5, we have x < 5.

Answer: B


Can someone please explain the "Since x^2 is nonnegative, we have 5 - x^2 <= 5". I can only solve (2) by substituting numbers. ScottTargetTestPrep
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   02 Jun 2021, 12:46
ScottTargetTestPrep wrote:
AbdurRakib wrote:
Is x<5 ?

(1) x^2 > 5

(2) x^2 + x < 5


We need to determine whether x < 5.

Statement One Alone:

x^2 > 5

If x = 3, then x is less than 5. However, if x = 6, then x is not less than 5. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x^2 + x < 5

Thus, we have x < 5 - x^2. Since x^2 is nonnegative, we have 5 - x^2 ≤ 5. Since x < 5 - x^2 and 5 - x^2 ≤ 5, we have x < 5.

Answer: B



Please explain in detail as to how you are solving the second statement, especially how you arrived at 5 - x^2 ≤ 5.
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   19 May 2023, 01:30
To determine whether x is less than 5, we can evaluate the statements (1) and (2) separately.

Statement (1) x^2 > 5:
This statement indicates that the square of x is greater than 5. If x^2 is greater than 5, it means that x can be either positive or negative. For example, if x is 3, then 3^2 = 9, which is greater than 5. However, if x is -3, then (-3)^2 = 9, which is also greater than 5. Therefore, statement (1) alone does not provide enough information to determine whether x is less than 5.

Statement (2) x^2 + x < 5:
This statement suggests that the sum of x squared and x is less than 5. By rearranging the terms, we have x^2 + x - 5 < 0. This inequality is not easily solvable without further calculations. However, we can determine whether x is less than 5 by analyzing the quadratic equation x^2 + x - 5 = 0. If the roots of this equation are both less than 5, then the statement holds true. Calculating the roots of the equation, we find that they are approximately -2.791 and 1.791. Both of these roots are less than 5. Therefore, we can conclude that x is less than 5 based on statement (2).
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Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   19 Jul 2023, 21:45
Though, I got it wrong first. Here is my explanation by plugging values.

(1) x^2 > 5
x can be +10 or -10 to satisfy. Insufficient
(2) x^2 + x < 5
x can only be within range x<2 and X >-3 (Assuming fraction values as well). Sufficient.
Ans B.
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink] Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   16 Jan 2024, 10:21
Is x<5 ?

(1) x^2 > 5
this implies that x < -5 or x > 5.
For x < -5 ------ x< 5 - Yes
For x > 5 --------x < 5 - No
Not sufficient

(2) x^2 + x < 5
=> x(x+1) < 5
By plugging in values for x, we find that, this inequality is true for values of x in the range -> -3<x<2
For this range of x, x is less than 5.
Hence st2 is Sufficient.
Answer B
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink]
16 Jan 2024, 10:21
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