Latest CAT Aptitude Question SOLUTION: Find Smallest Number when divided by 7,8 and 9 leave remainder 5,4 and 2.

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(#M40037209) CAT Numerical Ability question Number System Keep an EYE

Find Smallest Number when divided by 7,8 and 9 leave remainder 5,4 and 2.

Asked In CAT Lovejeet Singh (10 years ago)

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Saraswathy  (10 years ago)

7a+5 = 8b+4 = 9c+2

First take
7a+5 = 8b+4
7a = 8b-1
Possible values of (a,b) satisfying the above eqn. is (1,1), (9,8),etc
Take (1,1) = 7
LCM(7,8)*n+12 [since 7a+5=8b+4=12]
From (1) nd (2), we get 56n+12
Now 56n+12 = 9c+2
56n+10 = 9c
"c" should be a multiple of "9".. So assign a value for n which satisfies the eqn...

56*4+10 = 9c
234/9 = c
c = 26

Substitute c=26
9*26+2 = 236

Hence 236 ...

Is this solution Helpfull? Yes (15) | No (2)  

Saraswathy  (10 years ago)

236

LCM(7,8,9)N+236
504N+236
Put N=0 to get the smallest value...

Ans : 236

Is this solution Helpfull? Yes (1) | No (2)  

Lovejeet Singh  (10 years ago)

Can u please explain how 236 came ??
answer is 234(i guess). u can recheck and please elaborate if possible.

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Lovejeet Singh  (10 years ago)

Saraswathy.....i guess u preparing for CAT....and so do I....please can i connect with u on mail....please ping me on lovejeet0707@gmail.com if feasible to u....!

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shalina  (9 years ago)

for the problems like this..there is formulae
N=k(d1d2d3)+(r1+r2d1+r3d1d2)
N-number we need find
k-constant from 0 to any integer
d1,d2,d3 are divisors
r1, r2, r3 are remainders
here we need find smallest number ri8 then consider k=0
so,
N=(5+4*7+2*7*8)
N=145
IS D ANS

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Abhishek Mohanty  (7 years ago)

7a+5=8b+4=9c+2

now b=(7a+1)/8--------------(1)

and b=(9c-2)/8--------------(2)


from eqn 1 the integral solutions of a & b:-

a=1 b=1
a=9 b=8
a=17 b=15
so b=1,8,15,...............(it is an A.P with d=7)------(3)

from eqn 2 the integral solutions of b & c:-

c=2 b=2
c=10 b=11
c=18 b=20
so b=2,11,20,..............(it is an A.P. wiht d=9)------(4)

from eqn 3 and eqn 4 we must get the value b same in both the eqns:-

b=b

--->1+(n-1)*7=2+(a-1)*9------(here n,a are any term of eqn3 and eqn4 respectively)-------(5)

-->a=(1+7n)/9
for lowest value of b we must get the lowest integral solution of n which is 5 and hence a=4

thus putting n=5 or a=4 in eqn 4 we get b=29

so the required number is 8b+4=236(ANS)

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