difficult questions

sukh wrote:MaryÂ’s annual income is $15,000 and JohnÂ’s annual income is
$18,000. By how much must MaryÂ’s annual income increase
so that it constitutes 55% of Mary and JohnÂ’s combined
income?
(A) $3,000
(B) $4,000
(C) $7,000
(D) $11,000
(E) $25,000
Answer C
Decreasing the original price of an item by 25% and then
decreasing the new price by z% is equivalent to decreasing
the original price by

(A) 0.25(1 + 3z/100 )

(B) 0.25(1 + z/100 )

(C) 0.25(1 - 3z /100 )

(D) 0.75(1 - z/100 )

(E) 0.75(1 + 3z/100 )

Answer A

We don't have any answer for 1st Question. Ans is 3150 as 55%*33000 leads to 18150!

for 2nd: Option A is the right Ans.

As we know 0.75 - 0.75*Z/100 => 1 - ( 0.25 + 0.75*z/100 )

sukh wrote:MaryÂ’s annual income is $15,000 and JohnÂ’s annual income is
$18,000. By how much must MaryÂ’s annual income increase
so that it constitutes 55% of Mary and JohnÂ’s combined
income?
(A) $3,000
(B) $4,000
(C) $7,000
(D) $11,000
(E) $25,000

We can plug in the answers, which represent the needed increase in Mary's income.

Answer choice C: 7,000.
Increased income for Mary = 7000+15,000 = 22,000.
New total income for Mary and John = 22,000+18,000 = 40,000.
Mary/Total = 22,000/40,000 = 11/20 = 55%.
Success!

The correct answer is C.

Decreasing the original price of an item by 25% and then
decreasing the new price by z% is equivalent to decreasing
the original price by

(A) 0.25(1 + 3z/100 )

(B) 0.25(1 + z/100 )

(C) 0.25(1 - 3z /100 )

(D) 0.75(1 - z/100 )

(E) 0.75(1 + 3z/100 )

Let original price = 100.
Price decreased by 25% = 100-25 = 75.
Let z=20.
Price further decreased by 20% = 75 - .2(75) = 60.
Total decrease = 100-60 = 40.
Decrease/Original = 40/100.

Now we plug z=20 into the answers to see which yields our target of 40/100.

Only answer choice A works:
0.25(1 + 3z/100)
= (1/4)(1 + (3*20)/100)
= (1/4)(160/100)
= 40/100.

The correct answer is A.