A clothing store's revenue last May was 6 percent less than its revenue last April. The store's revenue last May was greater than its expenses last May, and the store's revenue last April was greater than its expenses last April. Was the store's gross profit last May less than its gross profit last April?
Let the store's expenses last May be Em
Let the store's expenses last April be Ea
Let the store's revenue last April be R then
the store's revenue last May is equal to 0.94*R
Given: 0.94*R > Em and R > Ea.
Gross profit for the month of April = (R - Ea)
Gross profit for the month of May = ((0.94*R) - Em)
So the question can be rephrased to
'If R > Ea and 0.94*R > Em, Is ((0.94*R) - Em) < (R - Ea)'
1) The store's revenue last May was 2,400$ less than its revenue last April
R - (0.94*R)= 2,400
Is ((0.94*R) - Em) < (R - Ea)
Is Ea - Em < R - (0.94*R)
Is Ea - Em < 2,400 ?
We don't know! Statement 1 is insufficient to answer the question.
2) The store's expenses last May were 4 percent less than its expenses last April
Is ((0.94*R) - Em) < (R - Ea) ?
Is ((0.94*R) - (0.96*Ea)) < (R - Ea) ?
Is 0.04*Ea < 0.06*R ?
Is Ea < (1.5)*R ?
We know that Ea < R and R < 1.5 R, So Ea < 1.5 R!
So statement 2 is sufficient to answer the question.
Answer
2
p.s: Posted in a hurry, let me know if you find any errors.
