$$0<t<\inf inity$$
Statement 1: 3 is a factor of t/4
The factor of a number refers to all the number 'n' that can divide 'n' completely without a remainder.
If n= t/4, then 3 is a number that can divide t/4 without remainder
$$\frac{\frac{t}{4}}{3}=\frac{t}{4}\cdot\frac{1}{3}=\frac{t}{12}$$
For 't/4' to be divided by 3 without a remainder, 't' must be a multiple of 12 i.e 12/4 = 3; 3/3 = 1; 36/4 = 9; 9/3 = 3 etc.
All multiples of 12 = multiples of 3, hence, 't' is a multiple of 3. Thus, statement 1 is SUFFICIENT.
Statement 2: 4t+3 is a multiple of 3
The multiple of a number 'n' is that 'n' multiplied by either a positive or negative integer and must be divisible by n.
If n=3 and 4t+3 is a multiple of 3;
$$Therefore,\ \frac{4t+3}{3}=\frac{4t}{3}+\frac{3}{3}=\ \left(4\cdot\frac{t}{3}\right)+\frac{3}{3}$$
$$=\ \left(\frac{4}{1}\cdot\frac{t}{3}\right)+\frac{3}{3}$$
For 't' to be divisible by 3, it must be a multiple of 3.
If t=3, then 4t+3 = (4*3)+3 = 15 => Multiple of 3
If t=6, then 4t+3 = (4*6)+3 = 27 => Multiple of 3
If t=9, then 4t+3 = (4*9)+3 = 39 => Multiple of 3
Therefore, 't' is a multiple of 3. Statement 2 is SUFFICIENT.
Since each statement is SUFFICIENT ALONE, then the correct answer is option D.
Thanks
If t is a positive integer, is t a multiple of 3?
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Source: Beat The GMAT — Data Sufficiency |
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deloitte247
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