Hannah took a two-page multiple-choice test. She answered 85 percent

Question

Hannah took a two-page multiple-choice test. She answered 85 percent of the questions correctly on the first page and 25 percent correctly on the second page. If she answered 70 percent of the questions correctly on the entire test, approximately what percent of the questions she answered incorrectly were on the second page?

(A) 17%
(B) 22%
(C) 33%
(D) 56%
(E) 63%

(A) 17%
(B) 22%
(C) 33%
(D) 56%
(E) 63%

DaMa03 · Answer

let's say the test has 100 questions and x are on the second page.
Then she answered x*0.25 correct on the second page
and (100-x)*0.85 questions correct on the first page.
So overall: x*0.25 + (100-x)*0.85 = 70 (since 70% of 100 questions are correct in total).
Solve for x=25 -> 25 Questions are on the second page, from which 75% are incorrect: 25*0.75 = 18.75
We know that in total 70 are correct, therefore 30 are wrong.

So, percent of wrong answers on the second page is 18.75/30=62.5%

Answer E

sujoykrdatta · Answer

We know the accuracies:

85% on page 1 and 25% on page 2 and overall 70%

If we look at the deviations from the mean, we have

85-70=+15% on page 1
25-70=-45% on page 2

Since the deviations must cancel out, we must have thrice the number of questions on the first page compared to the second page

If we assume 300 questions on page 1 and 100 on page 2, number of wrong answers on page 1 is 15% of 300 = 45 and number of wrong answers on page 2 is 75% of 100 = 75

Thus, percent of wrong answers on the second page 
= 75/(45+75) × 100
= 62.5 %

Answer E

Vivek1707 · Answer

Key point in this question is to understand the question requirement.

The question requirement is ---> WHAT % of TOTAL incorrect answers were on page 2

Using allegations you get get the ratio of questions on first page to those 2nd page

i.e F /S = (70 - 25) / (85 -70)

i.e F / S = 45 / 15 i.e 3/1

Say the total number of questions were 100 out of which 75 were on first page and 25 on 2nd page

Now we know that out of 25 on the 2nd page 3/4 were incorrect

So the required percentage would be

25 * 3/4 * /30 = 5/8 which is 62.5 ~ 63%

shefali23 · Answer

Given Information:

Number of questions on Page 1 = x
Incorrect on Page 1 = 0.15x ----- (1)

Number of questions on page 2 = y -------- (2)
Incorrect on Page 2 = 0.75y

Total incorrect questions = 30% which translates to 0.3(x+y) ------ (3)

need to find out  ---> 0.75y/(0.15x + 0.75y)= 5y/(x + 5y) ------- (4)

Using (1), (2), and (3), 
0.15x + 0.75y = 0.3(x + y)
implying 3y = x

putting this into (4), we get 5y/8y = 62.5% 
 Answer (E)

Kinshook · Answer

Hannah took a two-page multiple-choice test. She answered 85 percent of the questions correctly on the first page and 25 percent correctly on the second page.

If she answered 70 percent of the questions correctly on the entire test, approximately what percent of the questions she answered incorrectly were on the second page?

Questions 
 First page 
 Second Page 
 Total 
 
  Answered correctly 
 85%f 
 25%s 
 85%f+25%s=70%(f+s) 
 
  Answered incorrectly 
 15%f 
 75%s

Total 
 f 
 s 
 f+s

85%f+25%s=70%(f+s)
15%f = 45%s
f = 3s

Questions 
 First page 
 Second Page 
 Total 
 
  Answered correctly 
 85%*3s 
 25%s 
 70%*4s= 2.8s 
 
  Answered incorrectly 
 15%*3s= .45s 
 75%s=.75s 
 30%*4s =1.2s 
 
  Total 
 3s 
 s 
 4s

The percent of the questions she answered incorrectly were on the second page = .75s/1.2s = 5/8 = 62.5% ~63%

IMO E

Hannah took a two-page multiple-choice test. She answered 85 percent

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Questions	First page	Second Page	Total
Answered correctly	85%f	25%s	85%f+25%s=70%(f+s)
Answered incorrectly	15%f	75%s
Total	f	s	f+s

GMAT Problem Solving (PS) Questions

Hannah took a two-page multiple-choice test. She answered 85 percent

Prep Toolkit

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My Rewards