Quant Boosters - Shashank Prabhu, CAT 100 Percentiler - Set 4
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Q28) A sum of money is distributed among certain people. The second person receives Re.1 more than the first, the third Rs. 2 more than the second, the fourth Rs. 3 more than the third, and so on. The first person gets Re.1 and the last person Rs. 67. What is the total number of people?
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General term is n(n-1)/2+1
first term is n(n-1)/2+1=1.... n=1
nth term is n(n-1)/2+1=67... n=12
Total 12 terms. Although, it would be far easier to write down the terms and then get the answer.
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Q29) Consider ab, a two digit number and it’s square cde, a three digit number. For how many values of ab is (a+b)^2 = c + d + e ? a, b, c, d and e are all positive integers
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c+d+e can be one or more among 1, 4, 9, 16, 25 only.
c+d+e=1, a+b=1, (10)^2=100
c+d+e=4, a+b=2, (11)^2=121, (20)^2=400
c+d+e=9, a+b=3, (30)^2=900, (12)^2=144, (21)^2=441
c+d+e=16, a+b=4, (31)^2=961, (13)^2=169, (22)^2=484
c+d+e=25, a+b=5, nothing is possible
Total 9 cases
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Q30) ab is a two digit positive number such that ab is divisble by a as well as b. Find sum of all possible values of ab (in numerical value)
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10a+b=ka
10a+b=mb
b=(k-10)a
10a+ka-10a=mak-10ma
k-mk+10m=0
k(1-m)-10(1-m)=-10
(k-10)(m-1)=10
(15,3)- 1 case (15)
(12,6)- 4 cases (12,24,36,48)
(11,11)- 9 cases (11,22,33...99)
Total 14 cases
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@shashank_prabhu a little elaboration on how n(x) = 2^x ?
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@shashank_prabhu but doesnt that repeat possible unit digits ?
shouldnt the unit digits be 10 only?
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@shashank_prabhu like i can choose any two numbers in c(100,2) ways
out of which all the cases from 01 to 91 [ c (10,2) ] * 4 are valid ?
which gives me 180 / 450
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___ | ___ | ___ | ___ | ___ | ___ | ___ | ___
There are a total of 8 steps represented by (___) and let the dash ('|') represent if he is stopping at the previous step.There are 7 such dashes. Each dash can take a 0 or 1. 0 indicates, he is stopping at the step immediately before it.
As each dash can take a 0 or 1, the number of ways is 128.
And as the maximum steps u can take is 6, the cases where he takes 7 steps at a time - given by (1,0,0,0,0,0,0) and (0,0,0,0,0,0,1)- and 8 steps at a time - given by (0,0,0,0,0,0,0)- are eliminated.Therefore it is 125.
