Annie has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Annie, 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?
Annie has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Annie and Doris have is a multiple of 4.	Choices:  A) None  B) IIIonly  C) and III only  D) and III only  E) II, and III
Given that:   A=3D;   J=D+7;   After increase:   Alice: A=3D+4;   Jane: J=D+11;   Doris: D+4.   Analyze each option:   Alice has more stamps than Jane.   3D+4&gt;D+11 --&gt; D&gt;7/3=3.5. Thus this statement will be true if D is more than or equal to 4. Since we don't know that, then this statement is not always true.   Jane has 3 more stamps than Doris.   D+11=(D+4)+3. This is not true for ANY value of D.   The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.   The sum of the numbers of stamps that Alice and Doris have is (3D+4)+(D+4)=4D+8=4(D+2). So, this sum is a multiple of 4 for ANY value of D, which smeans that this statement is always true.   Answer: IIIonly (III only).
<result>B</result>
Annie has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Annie, 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?
Annie has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Annie and Doris have is a multiple of 4.