Companies A and B are part of the same industry and are located in the

Question

Companies A and B are part of the same industry and are located in the same city. For Company A, the average (arithmetic mean) salary of its employees, in United Arab Emirates dirhams (AED), is 10,000 AED higher than that for Company B. However, more than half of the employees at Company A have salaries below the average for Company B.

Statement: If the average salary at Company B is  ___1___ , then the median salary at Company A is  ___2___ .

Select for  1  and for  2  the options that complete the statement so that it most accurately reflects the information provided. Make only two selections, one in each column.

KarishmaB · Accepted Answer

The question is both - simple and tricky. The concept involved is very simple but when we go to pick options, there is a good chance that we will pick the incorrect ones because of how they are worded. Sometimes, we are specifically asked to pick two different options but not here. Hence, it is harder to think of picking the same option for both. We are given: However, more than half of the employees at Company A have salaries below the average for Company B. If more than half the employees at A have salaries lower than average salary of B, we know that Median of A < Mean of B If the average salary at Company B is greater than 100,000 AED , then the median salary at Company A is 100,000 AED or less . (not an option) If the average salary at Company B is less than 100,000 AED , then the median salary at Company A is less than 100,000 AED. Certainly True. ANSWER If the average salary at Company B is equal to 110,000 AED , then the median salary at Company A is less than 110,000 AED ( Not an option) If the average salary at Company B is between 100,000 and 110,000 AED , then the median salary at Company A is _____ There is some confusion here. It is not mentioned whether the extreme values are inclusive or exclusive. So answer could be "less than 100,000" (an option) or "100,000 or less" (not an option). If the average salary at Company B is between 100,000 and 110,000 AED , then the median salary at Company A is less than 100,000. Hence I cannot say for sure whether this statement will be true. If the average salary at Company B is greater than 110,000 AED , then the median salary at Company A is 110,000 AED or less. (Not an option) Here is another discussion on how to solve TPA questions: https://youtu.be/O-iV8Vv4svY

Sans8 · Answer

Given,
 More than half of the employees at Company A have salaries below the average for Company B. 
Hence, the median salary would also be less than the average for company B.

Now, looking through options
if,
>> If the average salary at Company B is  greater than 100,000 AED 
 Then, median can be anything either greater or less than or equals 100,000 AED.
 Hence no option satisfying it. In a similar way if we check logically through all options
Only  less than 100,000 AED  satisfies.

If the average salary at Company B is  less than 100,000 AED  than median will also be less that 100,000AED

sherlocked221B · Answer

KarishmaB   chetan2u   MartyMurray   Bunuel   bb

Can someone please explain why this is not the answer? I applied the same reason to arrive at this solution.

Option 1 -  greater than 100,000 AED
 Option 2  - less than 100,000 AED

bb · Answer

Does this not answer your question?

Prove that it’s not true:

If the average salary at Company B is greater than 100,000 AED, Then, median can be anything either greater or less than or equals 100,000 AED.

KarishmaB · Answer

This is quite an interesting question and BB has given you great food for thought.

The way I think about it is this: 
From the argument I can make out that median of A is less than mean of B and that is all.

So if mean of B is less than 100k, then median of A is less than 100k too. - Definitely true

If mean of B is more than 100k (say it is 105k), median of A could be more than 110k (say it could be 102k) or it could be equal to 100k or it could be less than 100k (say 90k). Anything is possible.

Hence the answer is less than 100k for both.

It is so simple and yet so hard!! I visualise the number line and think in terms of left of 100k or right of 100k.

PeachSnapple1 · Answer

Relatively simple question. This is one of the few DI questions that don't have complex wordings.

[more than half of the employees at Company A have salaries below the average for Company B.] --> This sentence tells us that the median at company A is the salary of one of these guys.

Therefore, if we know the mean(B) < X (a certain amount), then according to the prompt, we know more than half of A has a salary less than < X. Thus, the median is also a number that is less than X.
Note that if mean(B) > X (a certain amount), we cannot infer what is the range of those low-earners in A. Let's say that an average employee in B earn more than $100K/year, we cannot say whether those low-earners in A earn >100K, 100K, or <100K.

When I was doing this question, I was pre-thinking of [equal to 110,000 AED] for blank 1; and [less than 110K] for blank 2. But sadly they don't have that option for blank 2

tryorcry · Answer

Please someone correct me if i am wrong - 
Lesson learned that in TPA, there could be many one-to-many pairs that can fit as solution, however, we need to select that ONE pair that is strictly one-to-one.
In this case:
if 1- less than 100K , only answer 2 can have is -less than 100K

if we choose any other option for 1, we can have many option which can be true for 2. 
Like if 1- greater than 100K , 2 can be - Less than 100K , Equal to 110K etc. which cant be right.

Bunuel · Answer

Your “one to one” takeaway is right, but the reason is simpler:

We are told: more than half of Company A’s employees earn below Company B’s average. That means the median at Company A must be below Company B’s average (because the median is the point where at least half are at or below it).

So whatever you pick for 1 (Company B’s average), 2 must be “less than that value.” Among the choices, the only time you can force a single specific choice for 2 is when 1 is “less than 100,000 AED,” because then the only compatible option for 2 is also “less than 100,000 AED.” For the other 1 options, several 2 options could still be below B’s average, so they do not give a unique pair.

Companies A and B are part of the same industry and are located in the

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1	2
		greater than 100,000 AED
		less than 100,000 AED
		equal to 110,000 AED
		between 100,000 and 110,000 AED
		greater than 110,000 AED

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