Tough GRE® Math Questions

[Yoazzole]

Found these on mygretutor.com : Very good for practice

1)
Column A

A box contains 32 short pencils and 12 long pencils. The probability of picking 2 pencils, the first of which is short and the second one is long.

Column B

30%

2) 2x + 4y = 16
3x + 6y = 30
Column A

|x|

Column B

|y|

-I believe there is a mistake here. The first equation is the second equation divided by 3/2, but the numbers don't match on the right-hand side.

3) Column A

A vegetarian sandwich shop has a choice of 4 different sandwich toppings. The number of different types of sandwiches that can be made if at least one topping has to be used and each topping cannot be used more than once.

Column B
32

- I got 15, by adding 4 C 1 + 4 C 2 + 4 C 3 + 4 C 4 (where 4 C y stands for combination). But they say that's wrong.

I'm very worried about these questions. i would very much appreciate the help soon considering I am going to take the GRE very soon.

[Yoazzole]

Please answer the questions. I am in need of help very much.

[Kevinlee001]

#1, A= 32/44 times 12/43, compare then.
(sorry i am too lazy to do the calculation)
reason:there 32 short at the beginning chosen from totally 44pens, then choose a long one from the remaining 43 (44-1).
is this clear?

#2, i agree with you, as a mathematics student, the answer to this question is : no anwser in real number,(but ok is complex number). anyway, i would choose "not determined" for this one.
yeah, i hate the gre quan test, because i have seen a lot of them are stupid with mathematical mistake or unprecise statement.

#3, sorry, i really don't understand the question
"if at least one topping has to be used" to be use for what?
"each topping cannot be used more than once" more than once in what? in each sanwich?
and for the toppings, do you consider the up or down side?
in my view, up and down is the same thing.
this is a good example for what i said, "GRE quan test is stupid and not precise"
if i have to choose, i would say B is greater.

again, i wish you have good luck that without seeing the unprecise question.
even as a math major, i am not confident to get a perfect score, if these type of unprecise questions show up.

[WarriorOfDiscord]

1. 32/44 * 12/43 = 8/11 * 12/43 = 96/473 = 20% (approx)
2. Indeterminate. The problem is not solved in real space.
3. 15 is correct:
Let's say the four toppings are a, b, c and d.
a: You can make two classes of sandwiches- with and without 'a'
b: 2- with or without 'b'
c: 2
d: 2

There are 16 combinations (2*2*2*2). Since a sandwich must contain at least one topping (else it is just bread slices), the combination with none of the toppings should not be considered. So 15 sandwiches.

[Immortal]

@question 3:

I am sure A is supposed to be 33, since this is closest to B value (easier to miscalculate) and 33 results from 4! + 3! + 2! + 1!. This would be the case if you take the arrangement of the "toppings" into account. But I don't exactly know what a sandwich topping is so maybe I'm writing bullshit :D

I have to say it's lame that one has to complete the missing information in the questions by mindreading the test-writers - but then it's easy to mindread them, they are just like the bad guys in the movies: not very smart, evil and they want you to fail :(

[Neeshu]

2x + 4y = 16
3x + 6y = 30

multiplying equations by 2 and 3 respectively we get

6x+12y=48
6x+12y=60
----------------

well the equation given here is wrong you cannot have same values of x and y giving
different answers on right hand side.

[Bhanupratap]

hello friends,
i am bhanupratap,studied m.res in life sciences at glasgow university,.recently started gre preparation,.any one could suggest me some good material for quants. i appreciate you all,all the best
thanks

[Pivarela]

A vegetarian sandwich shop has a choice of 4 different sandwich toppings. The number of different types of sandwiches that can be made if at least one topping has to be used and each topping cannot be used more than once.

Answer:

If at least one topping has to be used means you will have sandwiches with 1,2,3,4 topping? Right,

So the total numbers of different types of sandwiches that can be made is
=(S 1 topping + S 2 topping + S 3 topping + S 4 topping)

S=sandwiches

S 1 topping= 4 (since we have 4 toppings) and so on,

If you can’t see that use the combination formula.

S 1 topping=4! / (4-1)! 1! =4

S 2 topping=4! / (4-2)! 2! =6

S 3 topping=4! / (4-3)! 3! =4

S 4 topping=4! / (4-4)! 4! =1 (remember 0! =1)

Total different sandwiches are 4+6+4+1=15.

Hope it helps,,

[GeneralVimes]

The problem with the third problem is that the sandwich with, let's say, lattice on onion and the the sandwich with onion on lattice are different sanwiches. So, to calculate the total number of sandwiches, we should use arrangements, not combinations.
number of arrangement of m items out of n ones is A(n,m)=n!/(m-n)!
A(4,1)=4
A(4,2)=12
A(4,3)=24
A(4,4)=24
Total 24+24+12+4=64>32.

[Waqas.Asim]

I have two questions please solve them:-

1. Two researchers spent a total of 35 hours on a certain project. One of the researchers spent 25 percent fewer hours on the project than the other.

Column A:

The difference between the number of house spent by each

Column B:

7

Column B is the answer

2. A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long. If the dimensions of the rug are in the same ratio as those of the floor, how many feet long is the rug?

Answer: 6√2

[GeneralVimes]

1. Two researchers spent a total of 35 hours on a certain project. One of the researchers spent 25 percent fewer hours on the project than the other.

It means, that if we take the second researcehr's time as 100%, the first one's time will be 75%. Therefore, the ratio if 75:100=3:4. So, we should divide 35 into the ration of 3:4. We'll get 15 and 20, their difference is 20-15=5<7

2. In order to solve this, we shold know about similarity of geomtry figures. If the dimensions of the rug are in the same ratio as those of the floor, they are called similar rectangles. And the areas of similar figures are in the same ratio as the squares of their linear measures. => The linear measures of similar figures are in the same ratio as the square roots of theis areas.

Here we have, that the area of the rug is twice smaller, that the floor, then, its length will be √2 times smaller, than the length of the floor. This gives us 12/√2=6√2

[Waqas.Asim]

Thanks for answering these questions. Your solutions are very helpful.

[GeneralVimes]

Welcome :)

[Lidiya]

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I want to speak with people . If I will speak I can learn more and more language
because this is important too much speak and improve language but I don't use this language and I can't speak very well.

[Lidiya]

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Why do you want to leave her here? I DON'T WANT TO tyler BARNETT RUBBED HIS FACE, THEN LET HIS HANDS FALL TO HIS LAP. She is onlly six years old. I dn't want to leave her anywhere, but I don't know what else to do. I can't get the kind of help she needs at home.