Math Problem 5

An apartment building has 5 floors, one of which has only 2 apartments. Each of the other floors has 4 apartments.

Compare two values:

Column A	Column B
3 times the number of floors in the building	The number of apartments in the building

Solution for GRE Analytical Problem 1:

Let’s name the patients B, C, D, E, F, G for their first letters. L will be used for lunch.

Let’s draw a table for sessions and fill it with known information:

• a lunch break at noon.
• Friedman will have the first session in the afternoon.

9:00	10:00	11:00	12:00	1:00	2:00	3:00
			L	F

Then we’ll make some notes to fix other pieces of information:

• Dawson's session must be earlier in the day than Edson's.

D – E

• Bernstein's session must be earlier in the day than either Edson's or Friedman's.

B – E

B – F

• Cox's session must immediately precede Grant's session.

CG

What preliminary conclusion cam we make of this?

1. We need two adjacent sessions for C and G
2. E can’t be neither on the first, nor on the second session (because both B and D must be before him)
3. B can’t be neither on the last, nor on the penultimate session (because he must be followed by both E and F)
4. D can’t be the last, for he must be followed by E
5. F can’t be the first, for he must be preceded by B

Restrictions 2-5 can be shown graphically:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
E F	E				B	B D

 

Now, we can proceed to Question I.

“Bernstein is only available at 10:00” means, that B will in the second slot

9:00	10:00	11:00	12:00	1:00	2:00	3:00
	B		L	F

Now, looking at the table, we can see only one pair of adjacent sessions for CG: at 2:00 and 3:00

9:00	10:00	11:00	12:00	1:00	2:00	3:00
	B		L	F	C	G

Then, as E can take the session at 9:00, he’ll take 11:00 session:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
	B	E	L	F	C	G

And the session at 9:00 is for D

9:00	10:00	11:00	12:00	1:00	2:00	3:00
D	B	E	L	F	C	G

So, we have only one way to schedule sessions if B is on 10:00.

Answer A

Note: we have not to check if D at 9:00 fits the requirements, because there isn’t 0 among possible answers. Otherwise, to judge between 0 and 1 we’d had to prove that D at 9:00 doesn’t violate any requirement.

Question II alters initial data:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
			L	C

Having place for C, we can see he place for G:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
			L	C	G

Session at 3:00 can’t be taken by F (because he switched to the morning), by B or by D. That’s why the last session must be taken by E.

9:00	10:00	11:00	12:00	1:00	2:00	3:00
			L	C	G	E

Since F can’t be the first, we have two possibilities for him:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
	F		L	C	G	E
		F

Then, we’ll place B before F

9:00	10:00	11:00	12:00	1:00	2:00	3:00
B	F		L	C	G	E
B		F
	B

And in every arrangement the place for D is clearly determined

9:00	10:00	11:00	12:00	1:00	2:00	3:00
B	F	D	L	C	G	E
B	D	F
D	B

Now we can see that in every case Dawson or Friedman has the third session of the day.

Answer D

We shall start solving Question III from our initial table with G added to 3:00 slot

9:00	10:00	11:00	12:00	1:00	2:00	3:00
			L	F		G

The place for C is determined:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
			L	F	C	G

Now, looking to restriction table we find place for E:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
		E	L	F	C	G

And we have two variants for B and D

9:00	10:00	11:00	12:00	1:00	2:00	3:00
B	D	E	L	F	C	G
D	B

Now we can see, that answer “(D) Edson has her session at 10:00” can’t be true;

Answer: D

Note: We could find this answer merely by looking at our restriction table, thus, saving precious time.

In Question IV there are two places for C (and for G, then):

9:00	10:00	11:00	12:00	1:00	2:00	3:00
C	G		L	F
	C	G

Then, place for B is determined:

9:00	10:00	11:00	12:00	1:00	2:00	3:00
C	G	B	L	F
B	C	G

Now we can see, that possibilities (A)-(D) are not necessary true. Then, correct answer if “(E) Dawson has a session at 2:00”. Really, as 3:00 slot is restricted for D, he can be placed only to 2:00 slot, and 3:00 session must be for E

9:00	10:00	11:00	12:00	1:00	2:00	3:00
C	G	B	L	F	D	E
B	C	G

Answer: E

See also these GRE problems: