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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x must be between which of the following pairs of integers? A. 3 and 8 B. 1 and 4 C. 3 and 12 D. 4/3 and 5/2 E. -5 and 1 The OA is B. In this PS question, I have to clear x of each inequality, right? Then I can get the values of x that meet the inequalities and those will be the solution. Experts, am I correct? Can you assist me with the solution, please? Thanks. ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 AAPL wrote: Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x must be between which of the following pairs of integers? A. 3 and 8 B. 1 and 4 C. 3 and 12 D. 4/3 and 5/2 E. -5 and 1 The OA is B. In this PS question, I have to clear x of each inequality, right? Then I can get the values of x that meet the inequalities and those will be the solution. Experts, am I correct? Can you assist me with the solution, please? Thanks. You can simply isolate x in each inequality. 1 + 3x > 4 3x > 3 x > 1 And 2x -3 < 5 2x < 8 x < 4 Together 1 < x < 4. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Quote:
Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x must be between which of the following pairs of integers?

A. 3 and 8
B. 1 and 4
C. 3 and 12
D. 4/3 and 5/2
E. -5 and 1

The OA is B.

In this PS question, I have to clear x of each inequality, right? Then I can get the values of x that meet the inequalities and those will be the solution.

Experts, am I correct? Can you assist me with the solution, please? Thanks.
Hi AAPL,
Let's take a look at your question.

$$1+3x>4$$
$$3x>4-1$$
$$3x>3$$
$$x>\frac{3}{3}$$
$$x>1 ... (i)$$

The next inequality is:
$$2x-3<5$$
$$2x<5+3$$
$$2x<8$$
$$x<\frac{8}{2}$$
$$x<4... (ii)$$

Combining (i) and (ii), we get:
1 < x <4
Which shows that the values of x must be between 1 and 4.

Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

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