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If a threedigit positive integer has its digits reversed, the
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07 Sep 2017, 03:57
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Fresh GMAT Club Tests' Challenge Question: If a threedigit positive integer has its digits reversed, the resulting threedigit positive integer is less than the original integer by 297. How many such pairs are possible? A. 3 B. 6 C. 7 D. 60 E. 70
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If a threedigit positive integer has its digits reversed, the
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Updated on: 17 Dec 2017, 02:49
IMO D
abc cba =297 100a+10b+c  (100c+10b+a) = 297 100(ac) +ca = 297 99(ac) =297 ac =3 b can take 09 => 10 values but c can not be 0 since reverse number is also 3 digit number c max = 6 because 6+3 =9 =a max so c can take 1,2,3,4,5,6 => 6 values Hence total numbers possible 6x10=60
D is the Answer
Originally posted by sahilvijay on 07 Sep 2017, 04:17.
Last edited by sahilvijay on 17 Dec 2017, 02:49, edited 2 times in total.




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If a threedigit positive integer has its digits reversed, the
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18 Sep 2018, 19:59
Bunuel wrote: Fresh GMAT Club Tests' Challenge Question: If a threedigit positive integer has its digits reversed, the resulting threedigit positive integer is less than the original integer by 297. How many such pairs are possible? A. 3 B. 6 C. 7 D. 60 E. 70 xyzzyx=297 297/99=3=xz 6 possible xz combinations: 96,85,74,63,52,41 10 possible y values: 09 6*10=60 possible pairs D



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Re: If a threedigit positive integer has its digits reversed, the
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07 Sep 2017, 05:39
Ans: D
N=100x+10y+z => (100x+10y+z)  (100x+10y+z) =297 => xz =3 (1) x <=9, z <=6 <=> Total 6 pairs z=1,2,3,4,5 & 6 (2) y can be 0 to 9(Total 10)
Total possibilities = 6*10=60



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Re: If a threedigit positive integer has its digits reversed, the
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07 Sep 2017, 04:55
Bunuel wrote: Fresh GMAT Club Tests' Challenge Question: If a threedigit positive integer has its digits reversed, the resulting threedigit positive integer is less than the original integer by 297. How many such pairs are possible? A. 3 B. 6 C. 7 D. 60 E. 70 100x+10y+z100z+10y+x=297 99(xz)=297 xz = 3 there are 6 possible numbers for x. for example: 9y66y9=297 and so on till x=4 as for y. there are 10 possibilities: from 0 to 9 so 6*10=60 pairs possible. so answer is D



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Re: If a threedigit positive integer has its digits reversed, the
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07 Oct 2017, 03:44
sahilvijay wrote: IMO D
abc cba =297 100a+10b+c  (100c+10b+a) = 297 100(ac) +ca = 297 99(ac) =297 ac =3 b can take 09 => 10 values but c can not be 0 since reverse number is also 3 digit humber so c can take 1,2,3,4,5,6 => 6 values Hence total numbers possible 6x10=60
D is the Answer What about a? b*c= 10 * 6= 60 so what about a? where have it gone?



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Re: If a threedigit positive integer has its digits reversed, the
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10 Oct 2017, 00:00
lor12345 wrote: sahilvijay wrote: IMO D
abc cba =297 100a+10b+c  (100c+10b+a) = 297 100(ac) +ca = 297 99(ac) =297 ac =3 b can take 09 => 10 values but c can not be 0 since reverse number is also 3 digit humber so c can take 1,2,3,4,5,6 => 6 values Hence total numbers possible 6x10=60
D is the Answer What about a? b*c= 10 * 6= 60 so what about a? where have it gone? No need to consider a  above solution is self explanatory



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Re: If a threedigit positive integer has its digits reversed, the
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11 Oct 2017, 16:56
Answer is D Possible combinations are 4b1, 5b2, 6b3,7b4,8b5, 9b6 B can be any dogit from 09 , hence 10 possiblities. and the above combination are only 6 , therefore answer is 6*10 = 60



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Re: If a threedigit positive integer has its digits reversed, the
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24 Dec 2018, 03:56
Bunuel wrote: Fresh GMAT Club Tests' Challenge Question: If a threedigit positive integer has its digits reversed, the resulting threedigit positive integer is less than the original integer by 297. How many such pairs are possible? A. 3 B. 6 C. 7 D. 60 E. 70 Par of GMAT CLUB'S New Year's Quantitative Challenge Set
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Re: If a threedigit positive integer has its digits reversed, the
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08 Oct 2019, 00:07
Bunuel wrote: Fresh GMAT Club Tests' Challenge Question: If a threedigit positive integer has its digits reversed, the resulting threedigit positive integer is less than the original integer by 297. How many such pairs are possible? A. 3 B. 6 C. 7 D. 60 E. 70 Asked: If a threedigit positive integer has its digits reversed, the resulting threedigit positive integer is less than the original integer by 297. How many such pairs are possible? Let the 3digit positive integer be of the form xyz (100x + 10y + z)  (100z + 10y + x) = 99(xz) = 297 x z = 3 Since x & z are not 0 (x,z) = {(4,1),(5,2),(6,3),(7,4),(8,5),(9,6)} = 6 cases y can take 10 values Total such numbers = 6*10 = 60 IMO D
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Re: If a threedigit positive integer has its digits reversed, the
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18 Nov 2019, 05:07
Bunuel wrote: Fresh GMAT Club Tests' Challenge Question: If a threedigit positive integer has its digits reversed, the resulting threedigit positive integer is less than the original integer by 297. How many such pairs are possible? A. 3 B. 6 C. 7 D. 60 E. 70 \( ABCCBA=297:100a+10b+c100c10ba=297, 99(ac)=297, (ac)=3\) \((A,C)=(9,6;8,5;7,4;6,3;5,2;4,1)…(A,C)≠(3,0):C>0\) \((A,C)=6.pairs…B=(0,1,2,3,4,5,6,7,8,9)=10\) \(Total.cases:6*10=60\) Ans (D)




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