M01-22

I think this is a high-quality question and I agree with explanation.

I think the answer choices make this question a bit too easy.

The question asks "How many numbers that are xxx,x21" - obviously there would be one number for every 100, (and 10 for every complete 1000). So the real question is how many hundreds between the two numbers? You can immediately see that the difference between the hundreds digit is 9, and there is only one answer choice that ends in a 9. That means you can go for this one immediately without any calculation.

You can also simply subtract the two numbers which gives you 133900. This is 1339 * 100 and you have 1 number per 100

I feel a real GMAT question would throw in some "trip up" answers into the options, like 139 or 13390 or 1329, etc

I think this is a high-quality question and I agree with explanation. This is a good quality question. The explanation provided is appropriate.

chetan2u, Bunuel

I was trying to solve this question by 324721 to 458521 .. where last 2 digits are fixed.
From 324721 to 399999 -- we can have only 8 (2 to 9) *6(4 to 9) * 3 (7 to 9) = 144 numbers ( as 3 and last 2 digits are fixed).
Similarly from 400000 to 458521 .. we can have 6(0 to 5 for ten thousands digit) * 9 * 6=324 ways.
so total 144+324 =468 ways.
Although i understood the answer for the question given... i did not understand through my above approach where am i goiing wrong. could you please help with this

Hi...
You miss out on a lot of combinations this way..
Just one example..
From 324721 to 399999 -- we can have only 8 (2 to 9) *6(4 to 9) * 3 (7 to 9) = 144 numbers ( as 3 and last 2 digits are fixed).
So you have taken hundreds place as only 7 to 9..
But if you have a number 325121.. this is a valid number but in your approach is not valid because of you taken hundreds as only 7, 8 or 9..
You could this by taking..
324700 to 324999....1*1*1*3*1*1=3
325000 to 329999....1*1*5*10*1*1=50
330000 to 399999..1* 7*10*10*1*1=700
400000 to 449999...1*5*10*10*1*1=500
450000 to 457999....1*1*8*10*1*1=80
458000 to 458600.. 1*1*1*6*1*1=6

Total ... 3+50+700+500+80+6=1339

A

Hi in this question we can also solve by the following

we know that 324700 - 325000 we have 3
and in every 1000 we will have 10
then from 458000-458600 we have 6

so since in every thousand we have 10 the units digit shd be 3+6+0 = 9 and hence from the options we can choose A

I think this is a high-quality question and I agree with explanation.

Hi Bunuel, do you have additional questions that are similar to this one? Thank you in advance!

Check Constructing Numbers, Codes and Passwords Questions in our Special Questions Directory.

Hope it helps.

I think this is a high-quality question and I agree with the explanation.

I think this is a high-quality question and I agree with explanation.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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