sandeepk123 wrote:

What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 8 respectively?

A. 456780

B. 678910

C. 997479

D. 997918

E. 997920

Dear

sandeepk123,

I'm happy to respond.

My friend, it is very hard to write truly GMAT-like Quant questions. It's true that in a good GMAT question, it may look very complicated but involve an easy shortcut, as this one does. The shortcut here, though, is a bit too easy: the remainder when dividing by 10 has to be the units digit. Once one sees the shortcut, there is absolutely no work, and I imagine a large number of students will see this shortcut.

My friend, I don't know if you are familiar with the idea of

Item Response Theory. This is the science of what constitutes a truly high quality test question. The psychometricians who design the GMAT are experts in Item Response Theory. I only know a little about it myself. The gist is that a well-written question really strikes this delicate balance: many students find the question challenging, or are persuaded by incorrect trap answers, and only high performing students choose the correct answer. This question has an obvious right answer, but there is really no inducement for anyone, other than a blind guesser, to choose any of the other four answers. The questions would likely show similar performance among high performers and low performers. Thus, it is not an item that discriminates between users well.

There are many layers involved in writing a truly GMAT-worthy math question. It's not just a matter of being clever with the math itself.

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)