Vishlesh
How do we know r= positive number? As in options negative numbers are also given, why r cannot be equal to -1? Or does saying PQRS are digits (as in question) means only positive numbers?
Hello
Vishlesh,
I understand your doubt and I appreciate the fact that you thought about it and brought it forward.
There is actually more than just this one question that I need to explain here. The GMAC rolled out two versions of this question – one is old (the one you posted on) and the other is new (from
OG ‘21 onwards).
- Old Question - on GMATClub
- New Question – OG ‘21 onwards
Let’s begin with your question on the older version.
Old Question - on GMATClub In this version, choices D and E have negative integers {-1 and -2}. These choices were especially given to induce the doubt that you also have in mind presently -
“if S can be negative, R and other digits can probably be negative as well.”
But, as I said, it is just a means to create confusion and trap students who have conceptual gaps. Otherwise, think about it, have you ever seen a 3-digit number that looks like 8(-1)4 or 46(-1)? No, right?
By definition, digits are always
non-negative. Specifically, when we say digits, we only mean the integers from
0 to 9, inclusive.
So, for this question in fact, choices D and E should be the ones rejected right away! If you check the choice selection data for this question (on GC - above the question), you will see that very few people got trapped this way. Choices D and E got only 1% of all votes each.
New Question – OG ’21 onwards Now, in the Official Guides from 2021 and 2022, we have the same question BUT with different choices. This was most likely done to make the question more challenging since rejecting the negative choices was straightforward.
The new choices for the same question are:
- 3
- 4
- 5
- 7
- 9
Try this one out! Tell me how it goes. 😊
Hope this helps!
Best Regards,
Ashish Arora,
Quant Expert,
e-GMAT