Inequalities - GT & LT

[money9111]

If (a^2)b>1 and b<2, which of the following could be the value of a?

a. 1/2
b. 1/4
c. -(1/2)
d. -2
e. 2/3

Answer is D

this question is from the MGMAT Equations, Inequalities, & VIC's. The explanation in the book is confusing because it uses the GT and LT, which are Greater than and Less than... my question is how do you know when to switch from GT to LT?

[papgust]

I felt that backsolving is best and easy way for this question.

A. 1/2
1/4 * b > 1. This means that b must be > 4. But b < 2 in the question. Eliminate

B. 1/4
1/16 * b > 1. This means that b must be > 16. But b < 2 in the question. Eliminate

C. -1/2
1/4 * b > 1. This means that b must be > 4. But b < 2 in the question. Eliminate

D. -2
4 * b > 1. This means that b must be < 1 and satisfies b < 2 in the question. Correct

E. 2/3
4/9 * b > 1. This means that b must be > 9/4. But b < 2 in the question. Eliminate.

[money9111]

ok i didn't think to backsolve... i don't know if i like how the MGMAT guide explains it using GT and LT... but I think i'll be able to get it... it's just uncomfortable now

[okigbo]

I too don't like the GT and LT approach of the mgmat books.

I just reasoned it out. a^2 will be positive no matter what and since the solution is greater than 1, and we know that b is less than 2, b MUST equal 1. Therefore, the equation becomes a^2>1; which means a >1 or a<-1. Pick D and move on...

[money9111]

Lol okigbo I agree... Just move on and don't look back! Thanks guys for your explanations!

[shashank.ism]

If (a^2)b>1 and b<2, which of the following could be the value of a?

a. 1/2
b. 1/4
c. -(1/2)
d. -2
e. 2/3

Answer is D

this question is from the MGMAT Equations, Inequalities, & VIC's. The explanation in the book is confusing because it uses the GT and LT, which are Greater than and Less than... my question is how do you know when to switch from GT to LT?

I couldn't understand the question. what does it exactly mean???

[harsh.champ]

I felt that backsolving is best and easy way for this question.

A. 1/2
1/4 * b > 1. This means that b must be > 4. But b < 2 in the question. Eliminate

B. 1/4
1/16 * b > 1. This means that b must be > 16. But b < 2 in the question. Eliminate

C. -1/2
1/4 * b > 1. This means that b must be > 4. But b < 2 in the question. Eliminate

D. -2
4 * b > 1. This means that b must be < 1 and satisfies b < 2 in the question. Correct

E. 1/2
1/4 * b > 1. This means that b must be > 4. But b < 2 in the question. Eliminate

Hey papgust,
I think in order to solve quickly u took the wrong E option.E is "2/3" not "1/2".Anyways ,still we are getting b>2 by plugging a=2/3 ,but still ,had it been some other no. it could have spelled trouble.

Over here,putting a=2/3
(4/9)*b>1
i.e. b>9/4[GT does not change to LT as 4/9 is +ve and transposing it wouldn't affect the inequality sign]
which is not possible as b<2 in the question.Hence ,E can be eliminated.

[harsh.champ]

If (a^2)b>1 and b<2, which of the following could be the value of a?

a. 1/2
b. 1/4
c. -(1/2)
d. -2
e. 2/3

Answer is D

this question is from the MGMAT Equations, Inequalities, & VIC's. The explanation in the book is confusing because it uses the GT and LT, which are Greater than and Less than... my question is how do you know when to switch from GT to LT?

The basic rule to be kept in mind:- In addition and subtraction,the GT and LT signs will never change.
Ex:-3>2
3 + 5 > 2 + 5

or 11 < 13
-8 +11 < -8 +13

However in multiplication and division,if a -ve no. is multiplied with,then LT would change to GT and vice-versa.
Ex:- 3>2
(-1) x 3 < (-1) x 2 [-3 < -2]

Similarly it goes for division:-
6 > 2
Dividing by -2
6/-2 < 2/-2 (-3 < -1)

I hope this clears your doubts.

[papgust]

Hey papgust,
I think in order to solve quickly u took the wrong E option.E is "2/3" not "1/2".Anyways ,still we are getting b>2 by plugging a=2/3 ,but still ,had it been some other no. it could have spelled trouble.

Thank you for pointing it out. I've edited now.