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?
- We need two adjacent sessions for C and G
- E can’t be neither on the first, nor on the second session (because both B and D must be before him)
- B can’t be neither on the last, nor on the penultimate session (because he must be followed by both E and F)
- D can’t be the last, for he must be followed by E
- 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 |
|
|
|
|
|
|
|
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
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