DH99 wrote:

Two players Lampard and Essien had a certain number of chocolates with them.If Lampard had 10 more than half the number of chocolates than Essien had,was the number of chocolates with Essien more than 20?

Statement 1: The difference between the number of chocolates than Lampard and Essien had was less than 30.

Statement 2: The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essien.

Hi..

the equation we get is \(L=\frac{E}{2}+10\)

lets see the statements..

Statement 1: The difference between the number of chocolates than Lampard and Essien had was less than 30.EITHER \(L-E<30.....\frac{E}{2}+10-E<30.....\frac{E}{2}>-20....E>-40...\) basically means E>0 or E=0... so E could have any number..

OR \(E-L<30.....E-\frac{E}{2}-10<30.....\frac{E}{2}<40...E<80...\) again E could be LESS than 20 or EQUAL or MORE than 20

Insuff..

Statement 2: The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essienthis is second equation ..

we have TWO variables and TWO different equations, here we can find the answer inspite of an inequality as we are not looking for exact valueans can be found..

sufficient..

but lets find value..

\(L+E>\frac{5E}{2}.....L>\frac{3E}{2}\)

substitute in main equation..

\((>\frac{3E}{2})=\frac{E}{2}+10....\frac{3E}{2}<\frac{E}{2}+10......E<10\)

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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