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 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 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 51

Two researchers spent a total of 35 hours on a certain project. One of the researchers spent 25 percent fewer hours on the project than the other.

Column A	Column B
The difference between the number of house spent by each	7

Solution for GRE Math Problem 50:

The sandwich with, let's say, lattuce on onion and the the sandwich with onion on lattuce are different sanwiches. So, to calculate the total number of sandwiches, we should use arrangements, not combinations. number of arrangement of m items out of n ones is A(n,m)=n!/(m-n)!=n*(n-1)*(n-2)*...*(n-m+1) A(4,1)=4 A(4,2)=4*3=12 A(4,3)=4*3*2=24 A(4,4)=4*3*2*1=24 Total 24+24+12+4=64>32. Answer:A

GRE Math Problem 50

A vegetarian sandwich shop has a choice of 4 different sandwich toppings.

Column A	Column B
The number of different types of sandwiches that can be made if at least one topping has to be used and each topping cannot be used more than once.	32

Solution for GRE Math Problem 49:
There is the possibility for m=5 ,n=5, thus m=n. But there also can be m=1, n=25 and m
In general, the relation is unknown.
Answer:D

GRE Math Problem 49

m and n are positive integers mn = 25

Column A	Column B
m	n

Solution for GRE Math Problem 48:
Putting r=0, t=0 we have 0=0. Putting r=1, t=1 we have 10 > 6
Answer: D, unable to determine

GRE Math Problem 48

Compare:

Column A	Column B
5(r +t)	5r + t

Solution for GRE Math Problem 47:
x(x + y) + y(x + y) = (x+y)(x+y) = (x + y)²
Answer:C, they are equal

GRE Math Problem 47

Compare:

Column A	Column B
(x + y)2	x(x + y) + y(x + y)

Solution for GRE Math Problem 46:
(a + 2)(b + 3)=ab+3a+2b+6
(a + 3)(b + 2)=ab+2a+3b+6

Let's find the difference:
(a + 2)(b + 3)–(a + 3)(b + 2) = ab+3a+2b+6 – (ab+2a+3b+6) = a–b

 Since there are no restrictions for a and b, their difference can have any sign, then, answer is D, unable to determine
Answer:D

GRE Math Problem 46

Compare:

Column A	Column B
(a + 2)(b + 3)	(a + 3)(b + 2)

Solution for GRE Math Problem 45:
Just make calculations: 2*3+3*2=12
Answer: (C) 12

GRE Math Problem 45

6. If x = 3 and y = 2, then 2x + 3y =
(A) 5
(B)10
(C)12
(D)14
(E)15

Solution for GRE Math Problem 44:

The fraction , is bigger than if a > 2b and less than otherwise. The only fraction here which is less than is (E)
Answer: E

GRE Math Problem 44

Which of the following fractions is the LEAST?
(A)
(B)
(C)
(D)
(E)

Solution for GRE Math Problem 43:

As , then x=3y. Putting this to 3x-4y=5, we’ll get 9y-4y=5, y=1. Therefore, x=3
Answer:(D)

GRE Math Problem 43

If 3x-4y=5 and then what is x?
(A)-5y
(B)-5x
(C)1
(D)3
(E) 4

Solution for GRE Math Problem 42:

bd=3^ax3^c=3^a+c
Answer:(B)

GRE Math Problem 42

If 3^a=b and 3^c=d, then bd=
(A) 3^ac
(B) 3^a+c
(C) 6^a+c
(D) 9^ac
(E) 9^a+c


Solution for GRE Math Problem 41:
Let’s build this sequence: 1, 1x3-1=2, 2x3-1=5, 5x3-1=14, 14x3-1=41, 41x3-1=122 – this is the smallest term greater than 100. It is greater than 120
Answer:A

GRE Math Problem 41

The first term of a sequence is 1. Starting with the second term, each term is 1 less than 3 times the previous term.

Column A	Column B
The smallest number greater than 100 in the sequence	120

Solution for GRE Math Problem 40:

As we can see, the sum of the areas of two equilateral triangles whose sides are 10 is twice less than the area of one equilateral triangle whose sides are 20


Answer:B

GRE Math Problem 40

Column A	Column B
The sum of the areas of two equilateral triangles whose sides are 10	The area of one equilateral triangle whose sides are 20

Solution for GRE Math Problem 39:
If x was 90, AB would be a hypotenuse in the right isosceles triangle and its value would be .
And for x > 90, AB will be even longer.
Answer: A

GRE Math Problem 39

x>90

Column A	Column B
The length of AB	7

Solution for GRE Math Problem 38:
How many three-digit numbers are?
The first digit can be any of 9, the second - any of 10, so does the third. Total 9x10x10=900 combinations.

How many three-digit palindromes are?
The first digit can be any of 9, the second - any of 10, and the third one must be exactly the same as the first, thus, leaving only 1 possibility. Total 9x10x1=90.

The probability that a three-digit number chosen at random is a palindrome is 90x900=0.1
Answer: C

GRE Math Problem 38

A number is a palindrome if it reads exactly the same from right to left as it does from left to right.
For example, 959 and 24742 are palindromes.

Column A	Column B
The probability that a three-digit number chosen at random is a palindrome	0.1

Solution for GRE Math Problem 37:
If all 16 shirts had costed $10, total amount of money spent would have been $160. It is $27 less, than the actual amount. Since Each $13 shirt is $3 more expensive than $10 shirt, there were 9 $13 shirts and 7 $10 shirts
Answer: A

GRE Math Problem 37

A man buys 16 shirts. Some of them cost $13 each, while the remainder cost $10 each. The cost of all 16 shirts is $187.

Column A	Column B
The number of $13 shifts purchased	The number of $10 shirts purchased

Solution for GRE Math Problem 36:

If all the tickets hab been sold for $25, the total sum would be 25x11=$275, which is 275-227=.$48 less, than the actual amount of money. Since the $13 ticket is 25-13=$12 cheaper, theree were = 4 tickets for $13 and 11-4=7 tickets for $25.
 Answer: Column A is bigger

GRE Math Problem 36

Tickets to a concert cost $25 and $13. An agent sells 11 tickets for a total price of $227.

Column A	Column B
The number of $25 tickets sold	The number of $13 tickets sold

Solution for GRE Math Problem 35:
If a²=b, then .
Now, if a=1, then Column A = 2 > Column B = 1.
And if  a=2, then Column A = 1 < Column B = 4.
Answer: D, unable to define.