Solution for Questions GRE Analytical Problem 5, Part 2

Question IV

If S appears on a panel, that panel must consist of at least how many professors?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

C6: S => (NV)

And there are no more conditions that require more members.

Answer (A) 3

Question V

Which of the following is an acceptable group of professors for a panel?

(A) M, N, Q, R – violates C2: !(MNR)

(B) M, Q, R,T – is quite acceptable

(C) M, R, T, U  – violates C5: R <=> Q

(D) M, S, U, V – violates C6: S => (NV)

(E) N,R,T,U – violates C5: R <=> Q

Answer (A) M, N, Q, R

Question VI

Which of the following groups of professors can form an acceptable panel by doing nothing more than adding one more professor to the group?

(A) M, R, T

C5:R <=> Q

We must add Q and we’ll get an acceptable panel

(B) N,Q,M

C5:R <=> Q

We must add R/ But that panel would violate

C2: !(MNR)

(C) Q,R, S

According to

C6: S => (NV)

We must add both N and V

(D) Q,R,V

C4: V=>(MS) or (MU) or (SU) or (MSU)

We must add at least two members

(E) V, R, N

C4: V=>(MS) or (MU) or (SU) or (MSU)

We must add at least two members

Answer (A) M, R, T

Question VII

Of the group N, S, T, U, V, which professor will have to be removed to form an acceptable panel?

(A) N

(B) S

(C) T

(D) U

(E) V

This panel violates

C1:!(NTU)

So, we must remove one of them.

But the presence of N and V is required by S

C6: S => (NV)

Then, we must remove T

Answer (C) T

Solution for Questions GRE Analytical Problem 5, Part 1

Solution for Questions GRE Analytical Problem 5:

Let’s fix the conditions:

C1: N, T, and U cannot all appear on the same panel.

!(NTU)

In another form it can be written:

(NT)=>!V

(NU)=>!T

(TU)=>!N

C2: M. N, and R cannot all appear on the same panel.

!(MNR)

In another form it can be written:

(MN)=>!R

(MR)=>!N

(NR)=>!M

C3: Q and V cannot appear on the same panel.

!(QV)

In another form it can be written:

Q <=> !V

V <=> !Q

C4: If V appears on a panel, at least two professors of the trio M, S, and U must also appear on the panel.

V=>(MS) or (MU) or (SU) or (MSU)

Or, equivalent to this:

(!M!S) or (!M!U) or (!S!U)=>!V

C5: Neither R nor Q can appear on a panel unless the other also appears on the panel.

R <=> Q

From this follows:

!R <=> !Q

C6: If S appears on a panel, both N and V must also appear on that panel.

S => (NV)

Then,

!N or !V => !S

Now we can proceed to question solving.

Question I

Which of the following CANNOT appear on a panel with R?

(A) M

(B) N

(C) Q

(D) S

(E) T

C5: R <=> Q

C4: Q <=> !V

C6: !N or !V => !S

So, professor S CANNOT appear on a panel with R

Answer (D) S

Question II

Exactly how many of the professors can appear on a panel alone?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

C4: V=>(MS) or (MU) or (SU) or (MSU)

Professor V can’t appear on a panel alone.

C5: R <=> Q

Professor’s R and Q can’t appear on a panel alone.

C6: S => (NV)

Professor S can’t appear on a panel alone.

So, only four of them can.

Answer (D) 4

Question III

If neither V nor N appears on a panel, then which of the following must be true?

(A) M appears on the panel.

(B) Q appears on the panel.

(C) T appears on the panel.

(D) S does not appear on the panel.

(E) U does not appear on the panel.

C6: !N or !V => !S

Answer (D) S does not appear on the panel.

Analytical Problem 5

The planning committee of an academic conference is planning a series of panels using eight professors, M, N, Q, R, S, T, U, and V. Each panel must be put together in accordance with the following conditions:

N, T, and U cannot all appear on the same panel.

M. N, and R cannot all appear on the same panel.

Q and V cannot appear on the same panel.

If V appears on a panel, at least two professors of the trio M, S, and U must also appear on the panel.

Neither R nor Q can appear on a panel unless the other also appears on the panel.

If S appears on a panel, both N and V must also appear on that panel.

Question I

Which of the following CANNOT appear on a panel with R?

(A) M

(B) N

(C) Q

(D) S

(E) T

Question II

Exactly how many of the professors can appear on a panel alone?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

Question III

If neither V nor N appears on a panel, then which of the following must be true?

(A) M appears on the panel.

(B) Q appears on the panel.

(C) T appears on the panel.

(D) S does not appear on the panel.

(E) U does not appear on the panel.

Question IV

If S appears on a panel, that panel must consist of at least how many professors?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

Question V

Which of the following is an acceptable group of professors for a panel?

(A) M, N, Q, R

(B) M, Q, R,T

(C) M, R, T, U

(D) M, S, U, V

(E) N,R,T,U

Question VI

Which of the following groups of professors can form an acceptable panel by doing nothing more than adding one more professor to the group?

(A) M, R, T

(B) N,Q,M

(C) Q,R, S

(D) Q,R,V

(E) V, R, N

Question VII

Of the group N, S, T, U, V, which professor will have to be removed to form an acceptable panel?

(A) N

(B) S

(C) T

(D) U

(E) V

Solution for GRE Math Problem 71:

Peter's grade > Victor's grade

Georgette’s grade > Victor's grade

We can’t determine, which of these grades is higher

Answer:D

Analytical Problem 4

John purchased a toy for his young daughter. The toy included nine colorful plastic pieces in the shape of the numbers from 1 to 9. In examining these pieces he made the following observations:

• One piece is purple and two pieces each are red, green, yellow, and blue.
• The two red pieces are consecutive numbers.
• The number 4 is green.
• The two blue pieces are not consecutive numbers.
• Both the 1 and the 9 are yellow.
• The purple piece is not a number immediately greater than or less than either green piece.

Question I. If one of the red pieces is the number 3, what number is the other red piece?
(A) 2   (B) 4   (C) 5   (D) 6   (E) 7

Question II. If the number 5 is green, each of the following could be true EXCEPT

(A) The purple piece and one of the yellow piece are consecutive numbers.

(B) The number 6 is purple.

(C)  The two blue pieces and the purple piece are three consecutive numbers.

(D) The number 2 is red.

(E) The number 8 is red.

Question III. If the number 6 is green, which of the following could be true?

(A) The number 2 is blue.

(B) The number 3 is purple.

(C) The number 5 is red.

(D)The number 5 is purple.

(E) The number 7 is blue.

Question IV.Which of the following, if true, would enable you to determine the color of every number?

(A) The 2 is blue.

(B) The 3 is blue.

(C) The 5 is red.

(D)The 7 is blue.

(E) The 7 is green.

Solution for GRE Math Problem 51:
If we take the second researcher's time as 100%, the first one's time will be 75%. Therefore, the ratio is 75:100=3:4. So, we should divide 35 into the ratio of 3:4. We'll get 15 and 20, their difference is 20-15=5<7
Answer:B

Analytical Problem 3

A farm is divided into four fields designated as the North Field, the East Field, the South Field, and the West Field. For the new growing season, each of the fields will be planted with exactly one of four crops—corn, beans, barley, or oats— according to the following plan:

• The West Field must be planted with either barley or beans.
• At least one field must be planted with corn.
• If, in the previous year, a field was planted with beans, then it must be planted with beans again.
• If, in the previous year, a field was planted with either wheat or alfalfa, then it must be planted with oats.

 

Question I. Which of the following could be the crops planted?

	North	East	South	West
A	beans	corn	barley	oats
B	beans	barley	oats	beans
C	wheat	barley	oats	beans
D	oats	barley	corn	beans
E	alfalfa	corn	beans	beans

Question II. If, in one year, the East Field is planted with wheat and the South Field is planted with beans, which of the following must be true of the year immediately following?

(A) The North Field is planted with barley.

(B) The North Field is planted with corn.

(C) The West Field is planted with barley.

(D) The South Field is planted with oats.

(E) The East Field is planted with beans.

Question III. In the previous growing season, the West Field could have been planted with any of the following crops EXCEPT

(A) alfalfa

(B) beans

(C) barley

(D)oats

(E) corn

Question IV. If, in the previous growing season, the West Field was planted with corn and the other three fields were planted with oats, what is the minimum number of fields that must be planted with crops that are different from those planted there for the previous growing season?

(A) None

(B) One

(C) Two

(D) Three

(E) Four

Question V. If three of the four fields were planted with beans for the previous growing season, which of the following could also have been true of the previous growing season?

(A) Barley was planted in the West Field.

(B) Corn was planted in the West Field.

(C) The fourth field was planted with oats.

(D) The fourth field was planted with wheat.

(E) The fourth field was planted with beans.

Question VI. If, for the previous growing season, the North Field was planted with oats, the East Field was planted with beans, and the South Field was planted with alfalfa, which of the following must be true of the new growing season?

(A) Corn is planted in the North Field.

(B) Oats are planted in the North Field.

(C) Barley is planted in the East Field.

(D) Barley is planted in the West Field.

(E) Beans are planted in the West Field.

Solution for GRE Math Problem 16:

This problem doesn't need much calculation. Knowing that 2468=2000+400+60+8=2x³+4x10²+6x10++8 we can say that the columns are equal


Answer:C