#150

[GHong14]

Henry purchased 3 items during a sale. He received 20% discount on the regular price ofthe most expensive item and a 10% discount off the regular price of the tow other items. Was the total amount of the 3 discounts greater than 15% on the sum of the regular prices of the 3 items?

1) the regular price of the most expensive item was $50, and the regular price of the next most expensive itemw as $20

2) The regular price of the least expensive item was $15

[Frankenstein]

Hi,
From(1):Let the price of cheapest item be x, where x<=20
we need to check if 50*0.2+20*0.1+x*0.1 > (50+20+x)*0.15 i.e. is 12+(x/10) > (70+x)(0.15) ie is x<30
As, x<=20, x<30 as well
Sufficient
From(2):cheapest item is 15$. We know nothign about other two
Insufficient

Hence A

[cans]

let prices be p,q,r where r is the most expensive, and p is lease expensive.
20% off on r and 10% off on p,q
discount on p=10% of p = 0.1p
a)r=50,q=20
20% of 50 = 10.
10% of 20 = 2
Thus total discount on q and r is 12 and total price is 70
to find if (0.1p + 12) >.15*(70+p)
or p<30. We know that p is least expensive and thus p<20. Sufficient.

b)p=15
discount=.1*15=1.5
To find if (1.5+0.2r+.1q) > .15(15+r+q)
150 + 20r + 10q > 225 + 15r + 15q -> r>15+q.
We know r>q but r>15+q is not known. Insufficient
IMO A

[kunalm]

IMO A
x,y,z are the prices
we know x>y>z

To Prove : .2x+.1y+.1z > .15x + .15y + .15z or not
.05x > .05y + .05z or not
x > y + z or not
For a the parameters are x=50 , y=20 , now as z<y so z<20
Hence x > y+z (in this case )
Sufficient

For b
We can clearly see we can't show x>y+z or vice versa
Insufficient