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11 Oct 2022, 02:31
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A
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Difficulty:
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38% (02:42) correct
62%
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wrong
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Positive integers a, b and c are all less than 10. If the sum of all the distinguishable three digit numbers that can be formed by juxtaposing these integers is 1332, is a = b?
(1) c = 3
(2) a = 2
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Similar question: positive-integers-a-b-and-c-are-all-less-than-10-if-the-sum-of-all-400001.html
(1) c = 3
(2) a = 2
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Similar question: positive-integers-a-b-and-c-are-all-less-than-10-if-the-sum-of-all-400001.html
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11 Oct 2022, 05:07
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Bunuel
Let us see the case when a=b.
1) a=b=c,
then the sum would be the number itself as only one number can be formed.
2) a=b and c is different
Total 3-digit number that can be formed is 3!/2!=3. aac, aca, caa
When you add them each digit gets added once => (100a+10a+c)+ (100a+10c+a)+ (100c+10a+a)
=> 222a+111c=1332……111(2a+c)=1332……2a+c=12
(1) c=3
2a+3=12……2a=9
Not possible
Sufficient
(2) a=2
a) When a=b…..2*2+c=12c=8, so Sum could be 822+228+282…..Possible a=b
b) When a is not equal to b…..a,b,c can be 2,1,3….
Insufficient
A
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11 Oct 2022, 15:43
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Bunuel
1) c =3, let's assume a=b, let a=b=5, in this case possible numbers are 553,535,355 sum of all these numbers is 1443, thus we can safely conclude that for all the values of a=b, greater than 5, the sum will be more than 1332, hence a, and b has to be less than 5. let's try a=b=4
possible values are 443,434,344 sum = 1221. since sum now is less than 1332, thus we can safely conclude for all values less than 4, sum will be less than 1332.
now since now value exist for the combination in which last digit is 3, and first two digit are equal we can safely conclude that a is not equal to B
A is sufficient
2) let's again assume a=b, let c=9 in this case possible values are 229, 292,922. now the sum of these numbers is 1443, which is greater than 1332, lets try c=8 in this case possible values are 228,282,822 now the sum of the numbers is 1332. which is a perfect match. now since we are getting both yes, and no as an answer thus B is not sufficient to answer this question.
Correct Answer should be A.
