When a certain number is divided by 12,18,24 the reminder is always 5 find the number

1 answer:

7 0

Let the number be N

then

N=12a+5 = 2*2*3*a+5

N=18b+5=2*3*3*b+5

N=24c+5=2*2*2*3*c+5

so

N-5=2*2*3*a

N-5=2*3*3*b

N-5=2*2*2*3*c

N-5 must be at least a multiple of 2*2*2 and 3*3. So 8*9=72 is a factor of N-5

In fact, it is the smallest. so the smallest N is 72+5=77

N-5 may have also other factors whose total multiplication is represented by the integer k:

N-5=72k

N=72k+5

Answer: The smallest number is 72
The number, in general, is 72k+5, where k is a positive integer.

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kirill [66]

So we are given the expression:

$\frac{mn^{2}}{4}$ ÷ $\frac{m^{2}n}{8}$

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$\frac{mn^{2}}{4} *\frac{8}{m^{2}n}= \frac{8mn^{2}}{4m^{2}n}$

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Which equation is true? I. (32 ÷ 8 – 2)6 = (32 – 1)2 II. 72 ÷ 9·4 = 62 ÷ (6 + 3) II only Neither I nor II I only I and II

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Answer: The answer is (b) Neither I nor II.

Step-by-step explanation: We are given two equations and we need to find which is true. Since it is a simple algebraic question, so we just need to follow BODMAS rule to check the equations.

The equations are as follows -

$(I)~~L.H.S=(\dfrac{32}{8}-2)6=(4-2)6=2\times 6=12.$