# 3 Hardest GRE Questions from April 2017

A GRE student with a 170 on the quantitative section last week shared that these were 3 of the hardest types of questions you could see on the test. Can you answer these? I have given the answers below and will share solutions once you give these a try.

**1.** Mary sold 15 widgets last week. The median sale price of all widgets was $130 and the average sale price of all widgets was $150.

**Quantity A:** $165

**Quantity B:** The least possible sale price of the most expensive widget.

**A.** Quantity A is greater.

**B.** Quantity B is greater.

**C.** The two quantities are equal.

**D.** The relationship cannot be determined from the information given.

**2.** Each student in a school takes either the French class or Spanish class, but not both. Each class has some male and some female students. The ratio of the number of female students to the number of male students is less for Spanish class than for French class.

**Quantity A:** The ratio of the number of female students to the number of male students in French class.

**Quantity B:** The ratio of the number of female students to the number of male students in the school.

**A.** Quantity A is greater.

**B.** Quantity B is greater.

**C.** The two quantities are equal.

**D.** The relationship cannot be determined from the information given.

**3.** Function f(100)= the product of all the even integers from 2 to 100, inclusive.

**Quantity A:** 40

**Quantity A:** The largest prime factor of f(100)

**A.** Quantity A is greater.

**B.** Quantity B is greater.

**C.** The two quantities are equal.

**D.** The relationship cannot be determined from the information given.

### Answers

1. B

2. A

3. B

Would you mind explaining these? The fact that I cannot solve these after 4 months of full time prep is kinda scary.

Explained above

Q1:- The sum of 15 widgets CP will be = 15 X 150 = 2250

As median is 130 so there will be 7 items whose CP will be less than or equal to this. To get the least greatest price, assume all are 130 then 8*130 = 1040

The remaining will have a sum of = 7 X A(Avg price)

Now 2250 – 1040 = 7 X A

A = 172

so Answer is B

Q2- Assume the ratio of Female to male in Spanish is 1/3 and French is 1/2. This satisfies the question condition.

A= 1/2 and B=2/5 so A is greater.

Q3- A = 40 and B=highest prime factor of f(100)

f(100) = 2 x 4 x 6 x …x 98 x 100

For B, 94 has factors 2, 47. 47 is prime Hence answer is B

Please explain 47. It is not an even iteger. Does it fall acc to condition? (Product of even integer). 2 is the only even prime factor.47 is prime but not even integer. Plz correct me if i am wrong

f(100) = 2 x 4 x 6 x …x 98 x 100

For B, 94 has factors 2, 47. 47 is prime Hence answer is B