GRE Math Problem 78

In the preceding figure, if l₁||l₂, what is the value of x?

(A) 36 (B)54 (C)90 (D)144 (E) 154

Solution for GRE Math Problem 77:
As the angle between the base of the triangle and the vertical line is not marked, the relation between x and y could be of any value. Answer:D

GRE Math Problem 77

Compare two values:

Column A	Column B
x	y

Solution for GRE Math Problem 76:

The value of this angle can be found as the sum of the angles a and b. As 20 minutes is 1 third of an hour, angle a is one third of 360 degrees, and equals to 120 degrees.
Then, angle b is two thirds of and angle between "11" and "12", then, it is two thirds of 30 degrees, which equals to 20 degrees.
Total 120+20=140 degrees
Answer: C

GRE Math Problem 76

Compare two values:

Column A	Column B
The measure, in degrees, of the smaller angle formed by the hour hand and the minute hand of a clock at 11:20	140

Solution for GRE Math Problem 75:

As he made a 25% profit on one painting, he sold it for 125% of the original price.
 $2000=125%
$1600=100% - its original price was $1600

As he had a 25% loss on the second painting, he sold it for 75% of the original price.

$2000=75%
$2666.(6)=100% - its original price was $2666.(6)

Last year Leo paid for both paintings $1600+$2666.(6)=$4266 and this year he got $4000 for selling them. So, he lost more than $100

  Answer:(C) He lost more than $100.

GRE Math Problem 75

Last year Leo bought two paintings. This year he sold them for ">2000 each. On one, he made a 25% profit, and on the other he had a 25% loss. What was his net loss or profit?
(A) He broke even.
(B) He lost less than $100.
(C) He lost more than "$100.
(D) He earned less than $100.
(E) He earned more than $100.

Solution for GRE Math Problem 74:
By what fraction is greater than ?

So, of the number is 7. Therefore, the whole number is 12.

But we were asked about the of this number, so, the answer is 12*3/5=20. Thank you for pointing this in comment :)

Answer:(D)20

GRE Math Problem 74

If of a number is 7 more then of the number. What is of the number?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 24

Solution for GRE Math Problem 73:
In order to determine the total number of players we have to multiply the number of players in one team by the number of teams in one division by the number of divisions. We’ll get dtp
Answer: (B) dtp

GRE Math Problem 73

The Center City Little League is divided into d divisions. Each division has t teams, and each team has p players. How many players are there in the entire league?
(A) d+t+p
(B) dtp
(C)
(D)
(E)

Solution for GRE Math Problem 72:
All the positive multiples of 5 less than 26 are: 5, 10, 15, 20, 25. Their average will be: =1+2+3+4+5=15
 All the positive multiples of 7 less than 26 are: 7, 14, 21. Their average will be: =14
Answer:A

GRE Math Problem 72

Compare two values:

Column A	Column B
The average (arithmetic mean) of all the positive multiples of 5 less than 26	The average (arithmetic mea: of all the positive multiples of 7 less than 26

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

GRE Math Problem 71

Peter's grade was higher than that of Victor.and Victor's grade was less than that of Georgette.

Column A	Column B
Georgette's grade	Peter's grade

Solution for GRE Math Problem 70:



Area=length x width

New Area=length x (1.25 width) = 1.25 (length x width) = 1.25 Area

Area will increase by 25%.


Answer:(A) 25%

GRE Math Problem 70

If the width of a rectangle is increased by 25% while the length remains constant, the resulting area is what percent of the original area?

(A) 25% 

(B)75% 

(C) 125% 

(D)225%

(E) Cannot be determined from the information given.

Solution for GRE Math Problem 69:

At what rate is the water filling the tank?
800-300=500 cubic feet
How many minutes will it take to completely fill a water tank?
3,750:500 = 7.5 minutes = 7 min. 30 sec.

Answer:(C) 7 min. 30 sec.

GRE Math Problem 69

How many minutes will it take to completely fill a water tank with a capacity of 3,750 cubic feet if the water is being pumped into the tank at the rate of 800 cubic feet per minute and is being drained out of the tank at the rate of 300 cubic feet per minute?
(A) 3 min. 36 sec.
(B) 6 minutes
(C) 7 min. 30 sec.
(D) 8 minutes
(E) 1,875 minutes


Solution for GRE Math Problem 68:

The legs of triangle BCE equal to the sides of the square ABCD. So, its area is the half of the area of ABCD. Thus,  the area of ABCD is 16

Answer:(C) 16

GRE Math Problem 68

 If the area of the triangle BCE is 8, what is the area of the square ABCD?
(A) 4
(B) 8
(C) 16
(D) 22
(E) 82


Solution for GRE Math Problem 67:
As and , then PQRS is a parallelogram. And as PQ=QR, it is a rhomb. Its obtuse angle equals 120 degrees, and the acute angle is 60 degrees. Then, triangle PQR is equilateral and PQ=QR=QP=3
Answer: (C) 3

GRE Math Problem 67

Here and .
If PQ=3 and QR=3, then what is the length of PR?
(A)
(B)
(C) 3
(D)
(E)



Solution for GRE Math Problem 66:
As the y-coordinates of A and B are equal, the distance between them is 2-(-4)=6. That’ll be the diameter of the circle. The radius of the circle is 3. Its area will be
Answer:(C) 9

GRE Math Problem 66

If A is the point (-4, 1) and B is the point (2, 1), what is the area of the circle which has AB as a diameter?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 36


Solution for GRE Math Problem 65:


1 < ab < 2
2 < a+b < 4

So, ab < 2 < a+b


Answer:B

GRE Math Problem 65

a < b

Column A	Column B
ab	a+b

Solution for GRE Math Problem 64:

As we can see, the circle whose diameter is a is located within the square whose side is a for any value of a. So, the square’s area is greater.


Answer: A

GRE Math Problem 64

a<1

Column A	Column B
The area of a square whose side is a	The area of a circle whose diameter is a

Solution for GRE Math Problem 63:
As

then



Let’s find the difference

Then c

Answer:B

GRE Math Problem 63

c and d are positive

Column A	Column B
c	d

Solution for GRE Math Problem 62:
Point (a,b) lays in the quarter where x<0 and y>0. So, a<0 and b>0 and b>a
Answer:B

GRE Math Problem 62

Column A	Column B
a	b

Solution for GRE Math Problem 61:
326(31)-326(19) =326(31-19)=326(12) – here we need not make any calculations, because there is only one answer which is more than 10 times greater than 326

Answer:(A)3,912

GRE Math Problem 61

326(31)-326(19) =

(A)3,912

(B)704

(C)100

(D)326

(E)10

Solution for GRE Math Problem 60:
  for x>0
Answer:B

GRE Math Problem 60

x>0

Column A	Column B

Solution for GRE Math Problem 59:

The perimeter of the square is
 Answer:(C) 3x + 4

GRE Math Problem 59

The length of each side of a square is
What is the perimeter of the square?
(A) x + 1
(B) 3x + 1
(C) 3x + 4
(D)
(E) It cannot be determined from the information given.

Solution for GRE Math Problem 58:

How much, in dollars, will receive the second one?
240-180 = 60

What is the difference between the amounts received by the two persons?
180-60=120

Answer: (C)$120

GRE Math Problem 58

A prize of $240 is divided between two persons. If one person receives $180, then what is the difference between the amounts received by the two persons?
(A) $30
(B) $60
(C)$120
(D)$210
(E)$420


Solution for GRE Math Problem 57:

Let’s take three consecutive integers: n-1, n, n+1
Their sum is n-1 + n + n+1 = 3n – is a multiple of 3.
Among the numbers given, only 28 is not the multiple of 3.


Answer:(C) 28

GRE Math Problem 57

Which of the following CANNOT be expressed as the sum of three consecutive integers?
(A) 18
(B) 24
(C) 28
(D) 33
(E) 36

Solution for GRE Math Problem 56:
What was Camille's total score?
75x6=450

What was Camille's total score after her teacher had dropped her lowest grade?
85x5=425

What was her lowest grade?
450-425=25
Answer:(B) 25

GRE Math Problem 56

Camille's average on her 6 math tests this marking period is 75. Fortunately for Camille, her teacher drops each student's lowest grade, and this raises her average to 85. What was her lowest grade?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50


Solution for GRE Math Problem 55:
The average of a, b, c, d, e,f, and g equals to their sum, divided by their quantity. So,

Answer: A

GRE Math Problem 55

Column A	Column B
The average (arithmetic mean) of a, b, c, d, e,f, and g	50

Solution for GRE Math Problem 54:
In a right triangle with the catheti of  3 and 4, the hypotenuse is 5. But there is no sign indicating that the triangle shown is the right one. So, c can be both greater than 5 (if the angle between the sides of 3 and 4 is obtuse) and less that 5 (if the angle is accute)
Answer: D

GRE Math Problem 54

Compare:

Column A	Column B
c	5

Solution for GRE Math Problem 53:

As the point (a,b) lays on the positive direction of X axis, a>0, b=0.

As the point (c,d) lays on the negative direction of Y axis, c=0, d<0

Then a + b=a>0 and c + d=d<0 and a + b> c + d

Answer:A

GRE Math Problem 53

Column A	Column B
a + b	c + d

Solution for GRE Math Problem 52:
In order to solve this, we should know about similarity of geometry figures. If the dimensions of the rug are in the same ratio as those of the floor, they are called similar rectangles. And the areas of similar figures are in the same ratio as the squares of their linear measures. => The linear measures of similar figures are in the same ratio as the square roots of theis areas. Here we have, that the area of the rug is twice smaller, that the floor, then, its length will be √2 times smaller, than the length of the floor. This gives us

 Answer:(D)