some questions in a written examination!
 

hey guys.I am getting a job.
I just took a written examination of big company.It was so terrible.
There are many question I did work out.
so here are some of them.
all of them are mutiple-choice.

1.Two kinds of chemical material are stored in six buckets(each bucket has only one kind of
chemical). The volumes of these buckets are: 8L, 13L, 15L, 17L, 19L and 31L. It is also known
that the price of one chemical is twice that of the other. A man has purchased five of the buckets,
and found that he spent the same amount money on each kind of chemical. Which bucket was left
unsold?
A. 8L
B. 13L
C. 15L
D. 17L
E. 19L

2.Four people are in a group
Alice says,”Exactly one of us is lying.”
Bob says, ”Exactly two of us are lying.”
Charles says, “Exactly three of us are lying.”
Dick says, “All four of us are lying.”
How many people in this group are lying?
A. 0
B. 1
C. 2
D. 3
E. 4

3.Allen and Brenda, both have a note stuck on their forehead, with a positive integer number written on it .Both Allen and Brenda can see each other’s number. They also know that the two numbers have a difference of one. They are trying to figure out the number on their own forehead.
Allen first says,”I don’t know my number.”
Brenda says,” I don’t know my number either”
Then Allen says “Now, I know my number”
Brenda now says, “Yeah, I know my number also!”
What is the number of Allen and Brenda?
A. 2,1
B. 1,2
C. 3,2
D. 2,3
E. 4,3

Plese explain to me if you can answer any of these above questions.
Thanks in advance.

"All four of us are lying." If this is a true statement, then Dick is not lying, so the statement is a false statement, simultaneously, e.g. there is a logical conradiction. So Dick is lying (at least one person is lying.) And At least one person is telling the truth, since not all are lying.

If exactly three are (truthfully) lying, then alice, bob, and dick are lying. Could be.

If exactly two are lying, then two are telling the truth. So there are two (different) exact numbers of people lying, which is impossible. (No two of the statements can simultaneously be true.)

If exactly one person is lying, it is Dick. So everyone else is telling the truth, and again, 1=2=3 is impossible.

The only plausible explanation is that Charles is telling the turth, and that there are three other liars in the group.

i dont think this one works (are you sure it isnt 32L ?).

8L, 13L, 15L, 17L, 19L and 31L

assumed prices:
chemical 1: $8, $13, $15, $17, $19 and $31
chemical 2: $16, $26, $30, $34, $38 and $62

chmical 1: $13 + $15 + $17 + $19 = $64
chemical 2: 31L = $62

so A. comes closest.

I've seen very similar questions to these, many years ago. Incidentally, if I may ask, what sort of job or company is this?

Sasha

this one seems not to have enough information ?

First I noticed that the total after leaving out a bucket must be divisible by three. The values mod 3 are 2,1,0,2,1,1 so to be divisible by three you must leave out a bucket with remainder 1, which is 13, 19 or 31, but 31 wasn't available, so only consider 13 or 19.

Second I added it up leaving out 13, getting the total 90. If that were right some set of buckets would add up to 30. But obviously not. Switching 19 for 13 subtracts 6, so 84, so need a set adding to 28, which is 13+15, so leave out bucket 19L.

If you're comfortable with numbers, doing that computation in your head is much faster than typing the description of doing it just was.

If he saw a 1 he would know he has a 2.
That means he doesn't see a 1

If she saw a 1 she would know she had a 2.
If she saw a 2 and knows Allen didn't see a 1 she would know she had a 3.
So she doesn't see a 1 or a 2.

If he saw a 2 he now knows he has a 3. If he saw a 3 he now knows he has a 4. Otherwise he doesn't know.

3,2 or 4,3

Is the question wrong or am I missing something?

is it the total volume or the total price that must be divisible by three (why) ?

can you please run thru your analysis assuming allan has a 42 and brenda has a 41.

Total volume. Because the volume is divided into two parts with equal costs but a two to one ration in price implying a one to two ratio in volume. Dividing a set of integers into parts with a one to two ratio of totals implies the overall total is divisible by three.

13L + 15L = 28L
8L + 17L + 31L = 56L

56L at some price is the same total cost as 28L at double that (per L) price.
28 + 56 = 84
84 is divisible by 3 and the probable couldn't work with a value that isn't.

Is that a joke? (Intent is hard to read in a forum post).

^ no. i understand how it works with numbers less than 4 but for large positive integers i cant see how they would find out their numbers

i guess the system only works for small integers.

thanks, i get it.

hehe, it is EMC.

It's not a system. There's only one pair of numbers for which that conversation makes sense (as with all these problems, assume they are both PLBs - Perfectly Logical Beings).

1. Allen declares that he does not know his number. We know Brenda doesn't have a 1, because if she did, there would only be one possibility for his number, and he would correctly conclude that he had a 2.
2. Brenda says the same. Now Allen knows that Brenda doesn't see a 1, because if she did, she'd use the same logic in the previous step and know her number.
3. Allen now says he knows his number. Since for all possible Brenda's numbers B (except for 1, which we know hers isn't), the only way Allen can assert that his number A = B - 1 or A = B + 1 would be if he knew one of those was false. The only possibility we have ruled out for his own number is 1, so the only way Allen can be sure of his number at this point is if Brenda has a 2. Thus, Allen must have a 3.
4. Brenda, also a PLB, has been following this. Since Allen declares that he knows his number, she runs through all of that and concludes that she has a 2.

The only valid solution for this is A = 3, B = 2. QED. :D