Hi Harsh,

Thanks for your reply.

Question states "Of the three-digit integers greater than 700" so it must be between 701 to 999.

Regards,
Uva

Here we can use a counting method in which we have 3 cases (XX means the same number)

Case1: XXY
First: We can choose 7,8 or 9 --> 3 options
Second: --> here we have only 1 option (see XX)
Third: We can pick any number except the number picked for the first digit --> 9
=> 3*1*9=27

CASE2: XYX
Same as above we have 3*9*1=27

CASE3: YXX
Same logic as above --> 3*8*1=24 (we can not choose 700 here because of the restriction >700) but in this case we eliminate options 800 and 900 which meets the requirement of the restriction >700 --> So we have here 24+2=26

Overall = 27+27+24=80 (C)

Method 2

#of arrangements of xxy =3!/2!
1st digit: 3 choices (7,8 or 9)
2nd digit: let's say same as 1st digit - 1 choice
3rd: any number other then the first 2 - 9 choices

--> 3!/2!*3*1*9=81 but we must substract 1 because we have included 700 in this calculation => 81-1=80 Answer (C)
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Topic Merged. It is not an absurd question. Refer to the above discussions.

Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822

Dear bablu1234,
I'm happy to respond, my friend.

I believe you already have gotten an good explanation of this particular math question. Bunuel is indeed a gifted teacher.

I want to point out something to you about the OG. The questions in the OG are released GMAT question: these questions are among the most rigorously examined questions on the entire planet. They went through several rounds of testing before they ever were on the GMAT, and they generated buckets of data while they were on the GMAT. By the the time any questions gets released from the GMAT and into an OG, it has a mountain of data behind its validity. By contrast, the explanations in the OG are only written when the book needs to be published, and when GMAC introduce additional questions in a new edition, some poor grad student somewhere has to produce new explanations. It's not clear to me that these explanations go through any feedback process at all. Some of the explanations are good, and some are simply atrocious. A few say things that are blatantly wrong. Most experts here on GMAT Club can give much better explanations than those that appear in the OG.

If the questions in the OG are like the crown jewels of Britain, the OG explanations are like costume jewelry one buys at a discount. If the questions in the OG are a world-class meal specially prepared by the finest chefs on earth, the OG explanations are like fast food. The difference in quality is mindboggling, and many students are entirely unaware of this difference because they are all bound in the same book with the same font.

Don't be fooled. Rely on the questions in the OG, but don't rely on the explanations. Get higher quality explanations here on GMAT Club, from Bunuel, Souvik, myself, and others.

Does all this make sense?
Mike
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Highlighted numbers do not fit.
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1. When tens digit equal to the hundreds digit, the number of possibilities for the units digit is 9 , for each possibility of hundreds digit for a total of 3*9=27
3. When units digit equal to the hundreds digit, the number of possibilities for the tens digit is 9 , for each possibility of hundreds digit for a total of 3*9=27
4. When tens digit is equal to units digit, there are 9 possibilities for each value of hundreds digit, for a total of 27,

So numbers, satisfying the constraints is (3*27)-1=80. 1 has to be subtracted because 700 is excluded.
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pattern can be aab, aba, or abb
aab: d1=3/3; d2=1/10; d3=9/10
aba: d1=3/3; d2=9/10; d3=1/10
abb: d1=3/3; d2=9/10; d3=1/10
3*(3*9*1)=81
81-1(for excluded 700)=80
C

pushpitkc hello , can please help me to wrap my mind around Bunuels`s solution

A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9);


I can not understand why second and third digits are 9 and 8 respectively, any idea?

Hi Bunuel

as per your explanation :

Numbers with all distinct digits = 3*9*8=216 (first digit can take 3 values - 7, 8, 9; second digit can take 9 values and the third digit 8 values);


how can these numbers be distinct, if first value is 7 then second digit can be any number from any of these sets: 0, 1, 2, 3, 4, 5, 6 7, 8, or this set( 1, 2, 3, 4, 5, 6 , 7, 8) what i am trying to say is that 7 can still be as second digit as well.... so if second digit take 9 values, 7 still can be among these 9 digits, why ? for example take this set as mentioned above 0, 1, 2, 3, 4, 5, 6 7, 8, there are 9 digits here, but as you see i simply replaced number 9 which is missing in this set with number 7

the same (my logic) applies to third digit...

pushpitkc could you explain why am i wrong ? please

Hi Bunuel,
Can you please explain how you got the highlighted part? Especially, 3*9*8?
Hundreds number can be 3 because there are only 3 possibilities, 7,8,9.
Tens number can be 0-9 = 10 numbers. But since one of these would be taken up by the 100's number, 10-1 = 9 possibilities.
Ones number can be 0-9 = 10 numbers. Since two of these would be taken up by 100's and 10's, 10-2 = 8 possibilities.

Therefore, 3*9*8 = 216.

Is my understanding right?
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