Compound Inequalities problems

Question

Concept: Compound inequalities 
 Question:  5! + 3 < a < 5! + 8
a) 3 < a < 8
b) 0 < a < 5
c) 3 < a- 5! < 8

GeneralEducation · Answer

ANSWER

3 < a-5! < 8

Don’t make the mistake of subtracting 5! From only first and last term and chosing option (a) as answer. Subtract 5! From all 3 terms, so

5! + 3 < a < 5! + 8
 Subtracting 5! From all 3 terms

3! < a- 5! < 8

Mantra: For compound inequalities (inequalities with more than one inequality sign) , perform operations on all terms together, not on first and last term alone.

GeneralEducation · Answer

Concept: Inequality signs
Question: Is ab < 0 if ac > 0 and bc < 0 ?
a) Yes
b) No
c) Can’t be determined

GeneralEducation · Answer

Answer Answer: Yes Since, ac > 0, both a and c are of same sign (both are positive or both are negative). Similarly bc < 0 implies b and c are of opposite signs. Combining both informations, we know now that b and a are of opposite signs. Multiplying these 2 numbers with opposite signs will yield a negative number, so ab < 0 Mantra: If x and y are of opposite signs , xy < 0 ; if x and y are of same signs then xy > 0

GeneralEducation · Answer

Concept: Factors
Question: Which of the following are the roots of y^3 – y = 0 ?
a) 1
b) 0
c) -1

georgenelson · Answer

Great I think this will be good experience to practice.

GeneralEducation · Answer

Sure George. You can also try out the GMAT diagnostic tool to get more questions:  https://goo.gl/LT72yk

All the best!!

GeneralEducation · Answer

Answer: All three

y^3 – y = 0
=> y (y^2 – 1) = 0 ( don’t divide both sides by y and conclude y^2 = 1 i.e y = 1, -1 only, this is wrong)
=> y (y-1) (y + 1) = 0
=> y = 0 , 1 , -1

Mantra: Don’t divide a variable on both sides of equation until you are sure that given variable is not equal to 0.

rajatjain14 · Answer

Thanks Neha for interesting set of questions.
I would like to specify an approach for solving cubic equations.

Approach to solve cubic equations  :

1. Go for hit and trial (Eg 0,-1,1,2,etc) to find the first root.
2. Then divide the complete equation by this factor.
3. Solve the remaining equation (possibly a quadratic equation) to find the remaining roots.

Example

x^3 - 6x^2 + 11x - 6 = 0 
Using Hit and trial, we get  x=1  as the root.

So, we get,  (x-1) (x^2 -5x + 6) =0

Solving  x^2 -5x + 6 = 0 ,

we get 2, 3 as the roots

Answer:  x = 1, 2 and 3

Compound Inequalities problems

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards