divelab/Sys2Bench huggingface dataset:
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?
Options:
A)34
B)40
C)68
D)88
E)92
Rationale: Given that length and area, so we can find the breadth.
Length x Breadth = Area
20 x Breadth = 720
Breadth = 36 feet
Area to be fenced = 2B + L = 2 (36) + 20 = 92 feet answer : E
Answer: E
Question: There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is
Options:
A)1/5
B)2/5
C)3/5
D)3/7
E)3/8
Rationale: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5
A
Answer: A
Question: The factorial expression 18!/12! is not divisible by which of the following integers?
Options:
A)3
B)5
C)19
D)14
E)9
Rationale: 18!/12! => 18 x 17 x 16 x 15 x 14 x 13
(A) 3 Can divide 18 or 15
(B) 5 Can divide 15
(C) 19 None of the Multiplicands present
(D) 14 Can divide 14
(E) 9 Can divide 9
Hence answer will be (C)
Answer: C
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment W that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
Options:
A)a. 3/5
B)b.2/3
C)c.7/10
D)d.3/4
E)e.4/5
Rationale: X(10) --- Net(0) --- W(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Answer: A
Question: If the ratio of x to y is 4 to 5, then (y-x)/(x+y)?
Options:
A)-7/3
B)-3/7
C)1/9
D)1
E)7/3
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 4 to 5 means
(x/y)=(4/5)
Cross-multiply
4x = 5y
x = (4/5)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (4/5)*y) / ((4/5)*y + y)
= ((1/5)*y) / ((9/5)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(1/5) / (9/5)
= (1/5) * (9/7)
The 5s cancel each other out, and you are left with 1/9.
Answer: C
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 7 years older than B, the present age of B is
Options:
A)35
B)37
C)39
D)41
E)42
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 7) years.
(x+7+10)=2(x—10)
hence x=37.
Present age of B = 37 years
Answer: Option B
Answer: B
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Options:
A)4
B)8
C)6
D)9
E)2
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer: A
Answer: A
Question: A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Options:
A)14 min
B)15 min
C)16 min
D)30 min
E)17 min
Rationale: Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
x/2 * 1/15 = 1 => x = 30 min.Answer: D
Answer: D
Question: A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
Options:
A)15 kmph
B)25 kmph
C)28 kmph
D)29 kmph
E)21 kmph
Rationale: B
25 kmph
[50/x + 50/(x/2)] – 100/x = 2
x = 25
Answer: B
Question: A sum of money is distributed among A,B,C,D in the proportion of 5:3:2:3. If A gets $1000 more than B, what is the C's share?
Options:
A)$2000
B)$5000
C)$8000
D)$1500
E)$1000
Rationale: Let the shares of A,B,C,D are 5x,3x,2x,3x
5x-3x = 1000
x = 500
C's share = 2x = $1000
Answer is E
Answer: E
Question: How many terms are there in 2, 4, 8, 16,..., 1024?
Options:
A)14
B)11
C)12
D)10
E)8
Rationale: 2, 4, 8, 16, ..., 1024 is a G.P with a =2
and r =4/2 =2
Let the number of terms be n. Then
2 x 2 ^n-1 = 1024
or 2^n-1 = 512 = 2^9
Thus n - 1 =9
n= 10
ANSWER:D
Answer: D
Question: A trumpet section includes three musicians. If they hold an audition to determine chair order within the section, and there are to be no ties, how many distinct chair orders can result?
Options:
A)240
B)125
C)120
D)100
E)6
Rationale: We have a word problem using permutations. We must identify the number of total items in the group. There are three possible musicians who could be placed in the first chair, two possible musicians for the second, one for the third. To determine the number of possible orderings, we multiply these numbers, which we can express as 3!. Now 3! = (3)(2)(1) = 6=E.
Answer: E
Question: What is the 14th digit to the right of the decimal point in the decimal equivalent of 82/11?
Options:
A)4
B)3
C)1
D)5
E)7
Rationale: 82/11 = 7.4545....
45 is non-repeating terminating decimal.
The 14th digit to the right of decimal point will be 5.
Answer D
Answer: D
Question: Find the area of a parallelogram with base 22 cm and height 21 cm?
Options:
A)462 cm2
B)478 cm2
C)490 cm2
D)268 cm2
E)668 cm2
Rationale: Area of a parallelogram = base * height
= 22 * 21
= 462 cm2
Answer: A
Answer: A
Question: If B takes 20% less time than A, to cover the same distance. What should be the speed of B, if A works at a rate of 10 km/hr?
Options:
A)12.5 km/hr
B)10 km/hr
C)15 km/hr
D)20 km/hr
E)25 km/hr
Rationale: Explanation:
S1 = 10 kmph
if T1 = 100
T2 = 80
10 x 100 = 80 x S2
S2 = 12.5 km/hr
Answer: Option A
Answer: A
Question: A sequence of numbers a1a1, a2a2, a3a3,…. is defined as follows: a1=3a1=3, a_2 = 5, and every term in the sequence after a2a2 is the product of all terms in the sequence preceding it, e.g, a3=(a1)(a2)a3=(a1)(a2) and a4=(a1)(a2)(a3)a4=(a1)(a2)(a3). If an=tan=t and n>2n>2, what is the value of an+2an+2 in terms of t?
Options:
A)4t
B)t^2
C)t^3
D)t^4
E)t^8
Rationale: An = (A1)(A2)......(An-1) = t
An+1 = t * An = t^2
An+2 = t * An * An+1 = t * t * t^2 = t^4
Answer: D
Answer: D
Question: If a boat goes 7km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is ?
Options:
A)13km/hr
B)52km/hr
C)85km/hr
D)2.8km/hr
E)5.98km/hr
Rationale: Rate upsteram =(7/42*60)kmph=10kmph.
speed of the stream =3kmph let speed in still water be xkm/hr. then speed upstream=(x-3)km/hr. x-3=10==>x=13km/hr Answer(A)
Answer: A
Question: The ratio between speed of the two trains is 7:8. If the 2nd train runs 400 km in 4 hrs, what is the speed of the 1st train?
Options:
A)87.9
B)87.5
C)87.7
D)87.6
E)43.3
Rationale: Answer: b
Explanation:
Speed of 2nd train = 400/4 = 100 kmph
Since the ratios are in 7 : 8
Speed of First train = 7/8 × 100 = 87.5 kmph
Answer:B
Answer: B
Question: Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?
Options:
A)2 : 3 : 4
B)6 : 7 : 8
C)6 : 8 : 9
D)4 : 6 : 8
E)None of these
Rationale: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
(140/100 * 5x), (150/100 * 7x) and (175/100* 8x)
7x, 21x/2 and 14x
The required ratio = 7x : 21x/2 : 14x
14x : 21x : 28x
2 : 3 : 4
Answer = A
Answer: A
Question: A loan shark made a loan of $100 to be repaid with $120 at the end of one month. What was the annual interest rate?
Options:
A)210%
B)220%
C)230%
D)240%
E)None of these
Rationale: Explanation:
r=I/PT
Answer: D
Answer: D
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of david, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?
Options:
A)1,008
B)1,296
C)2016
D)2,018
E)2,268
Rationale: Place A and E first: 8 options for D, 7 options for E.
We are left with 6 empty places. D, B and C must take first 3 places and F, G, H must take the remaining three.D, B and C can be arranged in their places in 3! ways. The same for F, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: C
Answer: C
Question: Two squares are chosen on a chessboard at random. What is the probability that they have a side in common?
Options:
A)1/18
B)64/4032
C)63/64
D)1/9
E)2/9
Rationale: In 64 squares, there are:
(1) 4 at-corner squares, each has ONLY 2 squares each having a side in common with...
(2) 6*4 = 24 side squares, each has ONLY 3 squares such that each has a side in common with...
(3) 6*6 = 36 inner squares, each has 4 squares such that each has a side in common with...
So we have the calculation:
P = (4/64)*(2/63) + (24/64)*(3/63)+ (36/64)*(4/63)
P = 1/18
ANSWER:A
Answer: A
Question: City X has a population 5 times as great as the population of City Y, which has a population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
Options:
A)1:8
B)1:4
C)2:1
D)4:1
E)10:1
Rationale: x= 5y, y= 2*z
X : Y , Y : Z
5 : 1 , 2 : 1
10 : 2 , 2 : 1
So, X : Z = 10 : 1
(E)
Answer: E
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 45kg. What is the weight of the new person?
Options:
A)75 Kg
B)65 Kg
C)85 Kg
D)80 Kg
E)60 KG
Rationale: Explanation:
Total increase in weight = 8 Ã— 2.5 = 20
If x is the weight of the new person, total increase in weight = xâˆ’45
=> 20 = x - 45
=> x = 20 + 45 = 65
Answer: Option B
Answer: B
Question: It takes John 15 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
Options:
A)8:50 a.m
B)8:00 a.m
C)7:50 a.m
D)6:50 a.m
E)9:50 a.m
Rationale: The time it takes John to get to work: time to walk to car park + time to drive
15 + 45 = 60 minutes = 1 hour
John needs to get out of the house 1 hour before 9:00 am at
9:00 - 1:00 = 8:00 a.m
correct answer B
Answer: B
Question: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 10 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
A)1/200
B)1/59
C)1/56
D)1/54
E)1/53
Rationale: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 10/100 = 1/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) Ã—(1/5) Ã— (1/10) = 1/200
Answer: A
Answer: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Options:
A)2/29
B)2/26
C)2/21
D)2/22
E)4/21
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: C
Question: A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes.12 sec to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and the length of the platform
Options:
A)120m
B)125m
C)132m
D)140m
E)150m
Rationale: Explanation:
Let the length of train be x metres and length of platform be y metres.
Speed of the train relative to man = (54 - 6) kmph = 48 kmph
= 48×(5/18) m/sec = 40/3 m/sec.
In passing a man, the train covers its own length with relative speed.
Length of train = (Relative speed × Time) = ( 40/3)×12 m = 160 m.
Also, speed of the train = 54 ×(5/18)m / sec = 15 m / sec.
(x+y)/15 = 20 <=> x + y = 300 <=> Y = (300 - 160) m = 140 m.
Answer: Option D
Answer: D
Question: Two trains 140 m and 200 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9 sec
B)10.1 sec
C)10.6 sec
D)10.8 sec
E)12.24 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 200 = 340 m.
Required time = 340 * 9/250
= 12.24 sec.
Answer:E
Answer: E
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
Options:
A)1000
B)2777
C)2976
D)2988
E)7122
Rationale: 2 * 22/7 * 1.75 * x = 11000
x = 1000
Answer: A
Answer: A
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 12),
what is the maximum possible area of C?
Options:
A) 6
B) 9
C) 24
D) 32
E) 64
Rationale: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
D
Answer: D
Question: The distance between two stars is 6.52 × 10^5 light years. What is the distance between the two stars in parsecs? (1 parsec = 3.26 light years)
Options:
A)2 × 10^5
B)4 × 10^6
C)5 × 10^7
D)7 × 10^7
E)9 × 10^8
Rationale: 6.52 × 10^5 ly / (3.26 ly/parsec) = 2 x 10^5 persec
The answer is A.
Answer: A
Question: The distance between two planets is 3.02 × 10^6 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
Options:
A) 9.3 × 10^5
B) 9.9 × 10^6
C) 9.3 × 10^7
D) 9.9 × 10^7
E) 10.1 × 10^8
Rationale: 3.02*10^6 light years = 3.02*10^6/3.26 parsecs.
3.02/3.26 is a little bit less than 1, something like 0.9, thus 3.02*10^6/3.26 = ~0.93*10^6 = 9.3*10^5.
Answer: A.
Answer: A
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
Options:
A)12.9
B)10.8
C)26.2
D)17.8
E)12.9
Rationale: Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Answer: B
Answer: B
Question: What is the greatest prime factor of 4^18 - 2^28?
Options:
A)2
B)3
C)5
D)7
E)127
Rationale: I'm happy to help with this.
We know 4 = 2^2, so 4^18 = (2^2)^18 = 2^(2*18) = 2^36
That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)
So, 4^18 - 2^28 = 2^36 - 2^28 = 2^(28 + 8) - 2^28 = (2^28)*(2*8) - 2^28 = (2^8 - 1) *(2^28)
= (128 - 1)*(2^28) = 127*(2^28)
The prime factors of 63 are 127, so the largest prime factor is 7, answer choice D.
Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/
Does all that make sense? Please let me know if you have any further questions.
Mike
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
E
Answer: E
Question: In 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date March 15, 1995 is a Monday, then which one of the following would the date March 15, 1996 be?
Options:
A)Monday
B)Tuesday
C)Friday
D)Wednesday
E)Friday
Rationale: From the information given,March 15, 1996 is 366 days after March 15, 1995.
366 days = 52 weeks and 2 more days. Therefore if March 15, 1995 is a Monday, then March 15, 1996 is Monday + 2 days = Wednesday
Answer: D
Answer: D
Question: 15c6+15c7+16c8=== 17cx
find x?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: 15c6=5005
15c7=6435
16c8=12870
15c6+15c7+16c8=17c9
ANSWER:D
Answer: D
Question: Find the value of X, Y by solving the below equations
X + Y = 16
X - Y = 14
Options:
A)16, 0
B)14, 2
C)15, 1
D)13, 3
E)11, 5
Rationale: X + Y = 16 ---(I)
X - Y = 14 -----(II) by adding (I) and (II)
------------
2X = 30 ==> X = 30/2 = 15
By Replacing the value of X in (I) we get 15 + Y = 16 ==>
Y = 16 - 15 = 1.
So, X = 15, Y = 1
Answer C) 15, 1
Answer: C
Question: A man's speed with the current is 16 km / hr and the speed of the current is 2 km / hr. The man's speed against the current is
Options:
A)8.5 km / hr
B)9 km / hr
C)12 km / hr
D)12.5 km / hr
E)None
Rationale: Sol.
Man's rate in still in water = (16 - 2) km / hr = 14 km / hr.
Man's rate against the current = (14 - 2) km / hr = 12 km / hr.
Answer C
Answer: C
Question: If $ 5,000 is invested in an account that earns 4% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
Options:
A)$ 4
B)$ 8
C)$ 12
D)$ 16
E)$ 432
Rationale: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.04/2)^2= 5404
Amount (SI) = P+PTR/100 = 5000+(5000*1*4/100)=5400
Difference = 5404-5400=4 $
A
Answer: A
Question: The price of a T.V. set worth Rs. 12000 is to be paid in 20 installments of Rs. 1200 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)29997
B)10800
C)27098
D)19000
E)2799
Rationale: Money paid in cash = Rs. 1200
Balance payment = (12000 - 1200) = Rs. 10800 .Answer:B
Answer: B
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph,then the speed of the boat in still water is :
Options:
A)4.2 km/hr
B)9 km/hr
C)13 km/hr
D)21 km/hr
E)None of these
Rationale: Solution
Rate upstream =(7/42x60)kmph = 10 kmph.
Speed of stream = 3 kmph.
Let speed in still water be x km/hr.Then, speed upstream =( x-3 ) km/hr.
∴ x - 3 = 10 or x = 13 km/hr. Answer C
Answer: C
Question: The cost per unit of electricity during a 4 year period is as follows:
Year 1, $2 per unit;
Year 2, $3 per unit;
Year 3, $4 per unit;
Year 4, $5 per unit.
If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?
Options:
A)$3.82
B)$3.62
C)$5.12
D)$3.12
E)$4.12
Rationale: Let money spent each year = $60
Units bought first year = 30
Units bought second year = 20
Units bought third year = 15
Units bought fourth year = 12
Total number of units = 77
Total money spent = 60*4 = 240
Average = 240/77 = 3.12
Answer : D
Answer: D
Question: If x and y are odd integers, which of the following must always be a non-integer
Options:
A)xy/4
B)xy
C)x/y
D)y/x
E)-xy
Rationale: as X and Y are odd, multiplication of x and y would result in odd integer
(Odd Integer)/4 will always be non integer
A
Answer: A
Question: A person walking at the rate of 5 km/hr crosses a bridge in 15 minutes. Find the length of the bridge
Options:
A)1200
B)1250
C)1224
D)1300
E)500
Rationale: speed = (5x5/18)m/sec
= 25/18 m/sec.
Dist 15 min(covered) =(25/18 x 15 x 60) ==> 1250 m
ANSWER B
Answer: B
Question: When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 0.2 centimeter. The actual diameter of the tissue, in centimeters, is
Options:
A) 0.005
B) 0.002
C) 0.001
D) 0.0005
E) 0.0002
Rationale: It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=0.2 then x=0.2/1000=0.0002.
The answer is E
Answer: E
Question: A car travels at a speed of 12 miles per hour. How far will it travel in 5 hours?
Options:
A)50 miles
B)60 miles
C)72 miles
D)22 miles
E)62 miles
Rationale: During each hour, the car travels 65 miles. For 5 hours it will travel
12 + 12 + 12 + 12 + 12 = 5 *12 = 60 miles correct answer B
Answer: B
Question: If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 35 overs in an ideal case scenario?
Options:
A)1158
B)1651
C)1653
D)1654
E)None
Rationale: Solution:
1158
Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 34th over. In the 35th over, he can hit a six in the last ball as well as that will be the last ball of his destination.
Thus runs for the 35th over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 34 + 36 = 1158
Answer A
Answer: A
Question: A box contains 4 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
Options:
A)2/3
B)1/2
C)5/8
D)3/5
E)3/4
Rationale: Each ball has an equal chance (1/10) of being selected fourth.
The probability that a black ball is selected fourth is 6/10 = 3/5.
The answer is D.
Answer: D
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 50
II. 70
III. 92
Options:
A)I only
B)III only
C)I and II
D)I​ and III
E)II and III
Rationale: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 50 --> 12 + 38 --> Possible
II. 70 --> Not possible
III. 92 --> 30 + 622 --> Possible
Answer: D
Answer: D
Question: The ratio of cats to dogs to birds to fish is 2:3:4:5. There are no other types of animals in the pet store.which of the followingcannotbe the total number of animals in the store?
Options:
A)28
B)42
C)56
D)70
E)77
Rationale: The parts add up to 2 + 3 + 4 + 5 = 14, so we know that any possible number of total answers must be a multiple of 14. All five answer choices are multiples of 14:
(A) 28 = 14*2
(B) 42= 14*3
(C) 56= 14*4
(D) 70= 14*5
(E) 77=not a multiple of 14
Answer: E
Question: Lally's internet provider offers unlimited traffic which costs $0.5 per day charged off at 12 a.m. The service is discontinued when client's debt exceeds $5. If today in the morning Lally makes a payment of $7, for how many days, including today, will she be connected to the internet without any additional payments, given her initial balance was $0?
Options:
A) 15
B) 24
C) 25
D) 26
E) 13
Rationale: day 0- payment of $7 is made in the morning (after 12 am midnight)
day 1 onwards(after 12 am midnight) internet service will begin and will run for 7*2=14 days i.e. at the end of day 15 balance will be zero.
now Lally can still use the internet till her debt reaches $5 which means total of 5*2=10 days.
now the question states for how many days, including today, will she be connected to the internet without any additional payments i.e. we will have to include day0 also in our final answer. therefore total no. of days =1+14+10=25=C
Answer: C
Question: A fair 2 sided coin is flipped 7 times. What is the probability that tails will be the result at least twice, but not more than 7 times?
Options:
A)119/128
B)120/113
C)114/210
D)121/141
E)104/117
Rationale: at least twice, but not more than 7 timesmeans exactly 2 times, 3 times, 4 times, 5 times, 6 times, 7 times
The probability of getting exactly k results out of n flips is nCk/2^n
7C2/2^7+7C3/2^7+7C4/2^7+7C5/2^7+7C6/2^7=119/128
Option: A
Answer: A