Alice has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Alice, Doris, and Jane each increase their number of stamps by 4, which of the following must be true after each person increases her number of stamps?
Alice has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.	Choose the correct choice from the following choices:  A) None  B) III only  C) I and III only  D) II and III only  E) I, II, and III
Let Alice, Doris and jane have A, D and J stamps initially.   We know that   A =3D   and   J=d+7   After addition of 4 stamps they'll have A+4, D+4, and J+4 stamps respectively.   Lets analyze each statements:   Alice has more stamps than Jane.   this can be written as   A+4 &gt; J+4   =&gt; 3D+4 &gt; D+7+4   =&gt;D &gt;7/3   It may not be true for many values of D.. D could very well be equal to 1,2 etc for which D&lt;7/3. Not correct.   Jane has 3 more stamps than Doris.   this can be written as   J+4 = (D+4)+3   =&gt; D+7+4 = D+4+3   Clealy not correct for any value of D.   The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.   (A+4)+(D+4) = 4k, where k is any integer   =&gt; 3D+4+D+4 =4k   =&gt; 4D+8 = 4K   =&gt; 4(D+2) = 4K   or K = D+2 .. clearly possible for any value of D. Hence Correct.   Hence Ans B. Only iii is correct.
<result>B</result>
Alice has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Alice, Doris, and Jane each increase their number of stamps by 4, which of the following must be true after each person increases her number of stamps?
Alice has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.