Problem Solving

During an auction, Jerome sold 75% of the first 1,000 items he offered for sale, and 30% of the remaining items offered for sale that day. If he sold 40% of the total number of items he ever offered for sale, how many items did Jerome offer for sale?

a) 750

B) 1050

C)1800

D)3500

E)4500

OA IS E. This is a very poorly worded question from grockit.com (i felt that way!!!)

Anyways request experts to assist.

So he sell 750 items (.75 x 1000) and the last is 30%. so .3x and all of that equal 40% of everything sold.

so 750 + .3x = .4(1000 + x). 750 + .3x = 400 + .4x; 350 = .1x; x = 3500. So 3500 is the remainder of items after the 1000. So total is [spoiler]3500 + 1000 = 4500 and therefore answer is E[/spoiler]

Whole auction = A=(1000+a)
%75 of first 1000 items= 1000.%75=750
Remaining= R= (1000 - 750 +a)= (250 +a)

750 + (250 + a)30%= (1000 + a).20%
a=4250

NOT 4500

pappueshwar wrote:During an auction, Jerome sold 75% of the first 1,000 items he offered for sale, and 30% of the remaining items offered for sale that day. If he sold 40% of the total number of items he ever offered for sale, how many items did Jerome offer for sale?

a) 750

B) 1050

C)1800

D)3500

E)4500

OA IS E. This is a very poorly worded question from grockit.com (i felt that way!!!)

Anyways request experts to assist.

oh i dont know how you solved it but here is my method...
consider X the items offered to be sold
0.75*1000 is the first items sold for 1000 items and 0.3 (x-1000) for the remaining items, both these equal 0.4 x
it would be
0.75*1000+0.3(x-1000)=0.4x
and the answer is 4500

pappueshwar wrote:During an auction, Jerome sold 75% of the first 1,000 items he offered for sale, and 30% of the remaining items offered for sale that day. If he sold 40% of the total number of items he ever offered for sale, how many items did Jerome offer for sale?

a) 750

B) 1050

C)1800

D)3500

E)4500

OA IS E. This is a very poorly worded question from grockit.com (i felt that way!!!)

Anyways request experts to assist.

Of the first 1000 items offered for sale, the number sold = .75(1000) = 750.
We can plug in the answers, which represent the total number of items offered for sale.
Since Jerome sold 40% of the total number of items offered for sale, and 40% of 1800 (answer choice C) is less than 750, eliminate A, B and C.

Answer choice D: 3500 items
Remaining items after the first 1000 = 2500.
30% of the remaining items sold = .3(2500) = 750.
Total percent sold = (750+750)/3500 = 150/350 = 3/7 ≠ 40%,
Eliminate D.

The correct answer is E.

Note that we had to plug in only ONE answer choice -- a very efficient way to solve the problem.