But here p is less than q , so time taken to produce p parts will be less by machine A than machine B which produce q parts that are more than p, so howcome : Qty A > Qty B ??

Please explain

We are making 1000 parts at a rate of \(p\) units/day and \(q\) units/day

Example:
p = 40 units/day
q = 50 units/day

which one is greater - \(\frac{1000}{40}\) or \(\frac{1000}{50}\) ?

.......
PS - This does not hold true is you assume p =98 and q=99. Because there is no definitive relationship between p and q, the answer can't be determined. The right answer IMO should be D

A does not hold true every time. If one assumes p =98 and q=99, the number of days for both is 11. And Because there is no definitive relationship between p and q, the answer can't be determined. The right answer IMO should be D

Hi There!

When you divide 1000 by 98 or by 99 you DO NOT GET THE SAME QUOTIENT. Let me try helping you with this. **Use calculator for precise values**.

\(\frac{1000}{99}=10.1010101010101--Machine B\)
\(\frac{1000}{98}=10.20408163265306--Machine A\)

So the above values are simply the time required to complete the work in days and the decimal value is the extra part of another day after the 10 days to finish the 1000 unit.
Because if we only consider 11 days then Machine A which does 98 units of work in 1 day will do 1078 units we do not need those extra 78 units, as the question only asks for 1000 units make sure you only find the value corresponding to 1000. Do no round off. Similarly, for Machine B.
Now, you tell me isn't 10.20>10.10. Just because these are some decimal values, we can't ignore them.


The Correct Answer is A because of the above reason. As it takes A more time as it does less units of work per day than B does.

Ask for further assistance.

P.S:. Welcome to the GRE Club

Hope this helps!

Hi,

I think you understood that if we compare with absolute values in your case, p=98, q=99 , of course A) is bigger in any case, but the question asks "days" , it may mean decimal part should be rounded up, so both your cases should be 11. Is my understanding about your post correct ?

Best,
Gocha

MinakshiS
Let us solve this without assuming any values!

We know \(p < q < 100\). Also that \(p > 0\) and \(q > 0\)

Col. A: \(\frac{1000}{p}\)
Col. B: \(\frac{1000}{q}\)

Since \(p\) and \(q\) are both positive, we can cross-multiply the denominators in both the columns;

Col. A: \(1000q\)
Col. B: \(1000p\)

Divide both the columns with 1000;

Col. A: \(q\)
Col. B: \(p\)

Now which one is greater?

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