Practice Questions Chat

a certain wire with a constant mass-to-length ratio has a mass of x grams per y centimeters of its length. which of the following is the mass of this wire, in kilograms, per meter of length?

x/10y

x/10y

Can someone help me with this question which i got in one of the practice exams i took: "If one of the integers is to be chosen from the integers 0 through 9 and if second number is to be chosen at random from integers 0 through 9, what is the probability that the two numbers will be even?"

Probability of both being even is 1/2 * 1/2 = 1/4

The set contains zero, the answer is 3/4

i just dont know how to get there

Is the question
- probability of both being even?
Or
- probability of their product being even?

The last line is a bit ambiguous in your question

the probability of their products being even

I framed the question exactly how i got it on my official gmat focus test

Not allowed to drop in an attachment otherwise would have been happy to share

Outcome from the first event -
Odd - 1/2
Even - 1/2
Same for the second.

No need to separate zero as multiplying zero will give you an even number only.
Zero is even fyi

So your favourable cases are
Odd and Even
Or
Even and Odd
Or
Even and Even

1/2*1/2 + 1/2 *1/2 + 1/2*1/2
= 1/4+1/4+1/4 = 3/4

Thankyou soo much! That helps!

You can also approach it by looking for atleast one even digit as the product will only be odd if both the digits are odd. So probability of selecting an odd digit - 1/2

probability of selecting two odd digits is - 1/2 * 1/2 = 1/4.

so probability of selecting two numbers to get a product even will be = 1 - 1/4 = 3/4

To get a job at Company X, an applicant must be recommended by three interviewers. Out of 30 applicants, 15 were recommended by the first interviewer 17 by the second interviewer, and 20 by the third interviewer. What is the least number of applicants who would have to have been recommended by all three interviewers
A 0
B 2
C 3
D 5
E 10

Can anyone tell me how to solve this please?

Think of this as a logical puzzle rather than a math problem.
Let's say the first interviewer recommended candidates numbered 1 to 15.
Now, when we try to think of which candidates were recommended by the second interviewer, we want to minimize the overlap. So, lets say they recommended candidates numbered 14 to 30.
There are now 2 candidates (numbered 14 and 15), who are recommended by 2 interviewers.
Now, when we try to think of which candidates were recommended by the third interviewer, we want to minimize the overlap with candidates recommended by both first and second interviewer. Basically, we want to try that the third interviewer does not recommend candidates numbered 14 and 15. Since the third interviewer recommends 20 candidates, this can easily be achieved if they recommend candidates numbered 1 to 10 and 21 to 30, for example.

Thus, the least number of applicants who would have to have been recommended by all three interviewers is 0.

Oh wow! thank you, SQ

three-interviewers-a-b-and-c-are-interviewing-118918.html?style=12#p961912

in this the total number of applicants exceeds the number recommended by the sum of all applicants. it doesn’t exactly apply - even though the answer is the same

30=17+15+20-Both-2*-all
30=52-Both-2*all
22=Both+2All
22-Both/2=All
We want to min All, so pick the highest value of both - in this case 22, which leads to 0.

where do you get this formula ?

excuse me, what does it mean “ all “ here ? is it 3-area overlapping or all about something you want to mention ?

and both also, can you specify it please ? thank you