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

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Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink]

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24 Jun 2017, 02:15
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74% (01:10) correct 26% (01:33) wrong based on 380 sessions

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Is x<5 ?

(1) x^2 > 5

(2) x^2 + x < 5
[Reveal] Spoiler: OA

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Md. Abdur Rakib

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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink]

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24 Jun 2017, 02:37
1
KUDOS
AbdurRakib wrote:
Is x<5 ?

(1) $$x^2$$>5

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

(1) $$x^2>5$$

If $$x = 6$$ or$$-6$$. $$x^2$$ will be greater than 5 in both cases.

However 6 is greater than 5 and -6 is less than 5.

(1) has multiple values. Hence I is Not Sufficient.

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

$$x(x+1) < 5$$

$$x<5$$ or

$$x+1<5 = x < 4$$

(2) has x less than 5 or 4. Therefore x is less than 5. II is Sufficient. Answer (B)...
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink]

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24 Jun 2017, 02:44
AbdurRakib wrote:
Is x<5 ?

(1) $$x^2$$>5

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

Solution:

Statement 1: x can be 3,4,5 or 10. Insufficient.

Statement 2: The greatest positive value that satisfies the equation is 1. Therefore, x<5 . Sufficient.

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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink]

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26 Jun 2017, 13:55
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Is x<5 ?

$$(1) x^2 > 5$$

This means x can have Positive and Negative values , lets check

$$x = 10 = x^2 = 100$$

$$x = - 10 = x^2 = 100$$

As we are getting answer as YES & NO

Eq. (1) =====> is NOT SUFFICIENT

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

$$x^2 + x < 5$$

$$x(x + 1) < 5$$

$$x < 5$$ or

$$x < 4$$

As both these values are < 5

(2) =====> is SUFFICIENT

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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink]

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17 Nov 2017, 11:38
1
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Expert's post
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.

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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5 [#permalink]

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18 Nov 2017, 15:39
AbdurRakib wrote:
Is x<5 ?

(1) x^2 > 5

(2) x^2 + x < 5

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variables and 0 equations, D is most likely to be the answer and so we should consider each of conditions first.

Condition 1)
$$x = 10$$ : Yes
$$x = -10$$ : No
This is not sufficient.

Condition 2)
$$x^2 + x < 5$$
$$x < 5 - x^2 < 5$$
This is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: Is x<5 ? (1) x^2 > 5 (2) x^2 + x < 5   [#permalink] 18 Nov 2017, 15:39
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