RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If X and Y are positive integers such that (3X + 7Y) is a multiple of 11, then which of the following will be divisible by 11?
A.4X + 6Y
B.X + Y + 4
C.9X + 4Y
D.4X - 9Y
Answer: D.4X - 9Y
Explanation: by hit and trail, we put X = 5 and Y = 1 so that (3X + 7Y)
= ((3*5) + (7*1)) = 22, which is divisible by 11
(4X + 6Y) = 4*5 + 6*1 = 26, which is not divisible by 11
(X + Y + 4) = (5 + 1 + 4) = 10, which is not divisible by 11
(9X + 4Y) = (9*5 + 4*1) = 49 which is not divisible by 11
(4X - 9Y) = (4*5 - 9*1) = 11 which is divisible by 11
(9X - 4Y) = (9*5 - 4*1) = 41 which is not divisible by 11
So the Answer is D
Question: A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.
I. The rate of X is Rs. 20 per kg.
II. The rate of Y is Rs. 13 per kg.
A.I alone sufficient while II alone not sufficient to answer
B.II alone sufficient while I alone not sufficient to answer
C.Either I or II alone sufficient to answer
D.Both I and II are not sufficient to answer
Answer: D.Both I and II are not sufficient to answer
Explanation: EXPLANATION
The ratio, in which X and Y are mixed, is not given.
So, both I and II together cannot give the answer.
answer is (D).
Question: What percentage of numbers from 1 to 70 have squares that end in the digit 1?
A.1
B.14
C.20
D.21
Answer: C.20
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such numbers = 14.
Required percentage = (14/70 * 100) = 20%
ANSWER:C
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,056. How much did she invest at 5%?
A.$500
B.$400
C.$700
D.$900
Answer: B.$400
Explanation: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1056/1000)-1 = 0.053 = 5.3%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.056
(0.05)x +0.06 - (0.06)x = 0.056
-0.01x = -0.004
x= -0.004/-0.01 = 4/10 = 40%
So X = 40% of the 1000 which is 400
ANSWER:B
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
A.288
B.660
C.500
D.267
Answer: C.500
Explanation: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.Answer: C
Question: Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y?
A.15.5 sec
B.8.4 sec
C.33.6 sec
D.31.11 sec
Answer: D.31.11 sec
Explanation: Z--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Question: A box contains SEVEN bulbs out of which 3 are defective. If TWO bulbs are chosen at random, find the probability that atleast one bulb is good
A.5/6
B.6/7
C.7/8
D.8/9
Answer: B.6/7
Explanation: Required probability ==1-3C2/7C2= 1 - 1/7 = 6/7.Answer:B
Question: The sum of the ages of 4 children born at the intervals of 1 years each is 12 years. what is the age of the youngest child ?
A.2.5
B.1.5
C.1
D.3.5
Answer: B.1.5
Explanation: Let x = the youngest child. Each of the other four children will then be x+1, x+2, x+3
We know that the sum of their ages is 12
so, x+(x+1)+(x+2)+(x+3) = 12
therefore The youngest child is 1.5 years old
Answer: B
Question: In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
A.187
B.190
C.192
D.195
Answer: D.195
Explanation: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1 = 195
D
Question: If (7)(x^2) has four different prime factors, at most how many different prime factors does x have?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: x can have at most 4 prime factors, namely the prime factor 7 plus 3 others.
If x had more than this number of prime factors, then (7)(x^2) would have more than 4 prime factors.
The answer is D.
Question: How many integers between 324,700 and 436,600 have tens digit 1 and units digit 3?
A.327
B.645
C.987
D.1119
Answer: D.1119
Explanation: The integers are:
324,713
324,813
etc...
436,513
The number of integers is 4366 - 3247 = 1119
The answer is D.
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 15 degrees?
A.π/3
B.3π/2
C.2π
D.5π/2
Answer: A.π/3
Explanation: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 15 degrees. 15/360 = 1/24.
Therefore length of arc = 1/24 * 8π = π/3 - Answer choice A.
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.143 per kg, the price of the third variety per kg will be
A.Rs.165.50
B.Rs.1700
C.Rs. 175.50
D.Rs. 180
Answer: A.Rs.165.50
Explanation: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-143/22.50 = 1 =â€º x - 143 = 22.50 =â€º x=165.50.
Hence, price of the third variety = Rs.165.50 per kg.
Answer A
Question: Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range?
A.3
B.4
C.cannot be determined
D.6
Answer: C.cannot be determined
Explanation: Yes, the correct answer is C
Question: If x^3 > y^2 > z, which of the statements could be true?
I. x < y = z
II. x = z < y
III. y < x < z
A.I only
B.III only
C.I and II only
D.II and III only
Answer: B.III only
Explanation: Given : x^3 > y^2 > z
I. x < y = z is not true i.e. Answers can not be Options A, C or E
II. x = z < y is not true i.e. Answers can not be Options A, C or E
III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options B
Answer: option B
Question: A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
A.$1520
B.$1640
C.$1780
D.$1850
Answer: A.$1520
Explanation: The total surface area is 2(2*4 +4*5 + 2*5) = 76 square feet
The total cost is 76*$20 = $1520
The answer is A.
Question: A person climbs up to a pole of 88 m high. In every min he climbs 12 m but slips down 8 m...how much time will he take to reach d top?
A.20th minute
B.21th minute
C.22th minute
D.24th minute
Answer: A.20th minute
Explanation: in every min person climbs up 12m and slips 8m . hence net displacement becomes 4m.
in 19 minutes person would climb (19*4)=76m
in 20th minute person would climb 12m up.. and it will be on top.
hence in 20th minute. person will reach on pole.
ANSWER:A
Question: If z is a multiple of 7899, what is the remainder when z^2 is divided by 9?
A.0
B.2
C.3
D.6
Answer: A.0
Explanation: The sum of the digits is 7+8+9+9=33.
Thus 3 is a factor of 7899, so 3 is a factor of z.
Then 3^3 = 9 is a factor of z^2.
Then the remainder when z^2 is divided by 9 is 0.
The answer is A.
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?
A.4/7
B.3/7
C.35/128
D.4/28
Answer: C.35/128
Explanation: using Binomial. theorem
nCr (p)^r (q)^n-r
7C4 (1/2)^4 (1/2)^r
which is 35/128
Answer is C.
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 83 more candidates got selected than A. What was the number of candidates appeared from each State?
A.7000
B.8300
C.6000
D.5000
Answer: B.8300
Explanation: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 83 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 83
=> total appeared candidates in State B = 83 x 100 = 8300
=> total appeared candidates in State A = total appeared candidates in State B = 8300
Question: What is the Mode of the following data set R- {1,2,7,9,6,6,7,7}
A.1
B.2
C.7
D.6
Answer: C.7
Explanation: Mode of a set is the data point that is repeated the most number of times. In the set given, 7 is repeated.
Answer: C
Question: 624 people are protesting outside of the White House. If they are standing in a rectangle in which the rows are no less than 6 people and no more than 104, how many different combinations of rectangular shapes are possible?
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: firstly factors of 624 = 1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
the question says each row will have people no less than 12 and no more than 52,
therefore, we should be interested in the factors between 12 and 52 (inclusive)
12(in each row) * 52(number of columns) =624, similarly
13 * 48
16 * 39
24 * 26
26 * 24
39 * 16
48 * 13
52 * 12
total possibilities = 8
option C
Question: The average age of a group of 10 students was 25. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
A.37 years
B.30 years
C.32 years
D.44 years
Answer: A.37 years
Explanation: The total age of 10 students with average 25 = 250
The total age of 12 students with average 27 = 324
The total age of 2 new students = 74
Their average =37
Correct Option A
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain?
A.45
B.50
C.55
D.60
Answer: D.60
Explanation: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 4*180/12 = 60 ounces of water
D
Question: Find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case.
A.170
B.172
C.174
D.176
Answer: C.174
Explanation: The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(31, 5) + 4 = 174.
ANSWER:C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.79
B.5.77
C.5.76
D.5.72
Answer: C.5.76
Explanation: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76.Answer:C
Question: At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: 39 = 19 + 18 + 12 - 4 - 2x
2x = 19 + 18 + 12 - 4 - 39
= 45 - 39
= 6
x = 3
ANSWER:B
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A.3/4
B.1/4
C.1/3
D.7/19
Answer: C.1/3
Explanation: Total number of balls = (8 + 7 + 6) = 21.
Let E	= event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E)=7
P(E)=n(E)/n(S)
=7/21
=1/3
The answer should be C
Question: For how many integers k is (k^2)+3 = 3+(2^k) ?
A.None
B.1
C.2
D.3
Answer: C.2
Explanation: (2^2)+3= 3+(2^2)
(2^4)+3= 3+(4^2)
For k= 2 and 4 the above equality holds true.
Answer:Option C
Question: There are two pipes which are functioning simultaneouly to fill a tank in 12 hours, if one pipe fills the tank 10 hours faster than other then how many hours second pipe will take to fill the tank ?
A.30 hours
B.35 hours
C.40 hours
D.42 hours
Answer: A.30 hours
Explanation: Explanation:
Lets suppose tank got filled by first pipe in X hours,
So, second pipe will fill the tank in X + 10 hours.
=>1/X+1/X+10=1/12
=>X=20
ANSWER IS A
Question: A train of length 180 metres takes 54 seconds to cross a tunnel of length 270 metres. What is the speed of the train in km/hr?
A.50 km/hr.
B.20 km/hr.
C.30 km/hr.
D.40 km/hr.
Answer: C.30 km/hr.
Explanation: Sol.
Speed = [180 + 270 / 54] m/sec = [450 / 54 * 18/5] km/hr =30 km/hr.
Answer C
Question: If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated?
A.24
B.60
C.720
D.520
Answer: C.720
Explanation: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (7-1)! = 6! = 720=C
Question: The number which exceeds 12% of it by 52.8 is:
A.60
B.77
C.269
D.26
Answer: A.60
Explanation: Explanation:
Let the number be x. Then, x – 12% of x = 52.8
x – (12/100)x = 52.8
x (1– 12/100) = 52.8
(88/100)x = 52.8
x = (100 X 52.8) / 88 = 60
ANSWER: A
Question: How many prime numbers are between 15/7 and 131/6?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: 15/7= 3-
131/6= 22-
Prime numbers between 3 and 22 are 5, 7, 11, 13, 17, and 19
- sign signifies that the number is marginally less .
Answer D
Question: A boy has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.60
B.110
C.140
D.130
Answer: A.60
Explanation: Let number of notes of each denomination be x.
Then x + 5x + 10x = 320
16x = 320
x = 20.
Hence, total number of notes = 3x = 60.
A
Question: What is the probability that their sum of two numbers, randomly selected from the set {3,6,9,12,15,18} will be greater than 9?
A.7/6
B.7/9
C.7/8
D.7/10
Answer: A.7/6
Explanation: First7 problem is 6C2 = 12 .. Not 20..
Point 2, you sum should be greater than 9, so these are the following possibilities you have
({3,9},{3,12},{3,15},{3,18},{6,9},{6,12},{6,15},{6,18},{9,12},{9,15},{9,18},{12,15},{12,18},{15,18}) which leads to 14 pairs
So the probability is 14 on 12 or 7/6..
ANSWER:A
Question: Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?
A.25/28
B.27/28
C.30/28
D.40/28
Answer: B.27/28
Explanation: There are 6 consonants and 2 vowels in KHANTKAR .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : B
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
A.11758
B.11759
C.11755
D.11750
Answer: D.11750
Explanation: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer: D
Question: Choose the missing terms out of the given alternatives.
CMW, HRB, ?, RBL, WGQ, BLV
A.MWS
B.MWG
C.SJE
D.HHW
Answer: B.MWG
Explanation: B
MWG
The letters move five steps forward.
Question: Which of the following will divide evenly into 407,406,520?
A.11
B.21
C.4
D.31
Answer: C.4
Explanation: Rule:
4: Last two digits should be divisible by 4
the last two digits are 00, which are divisible by 4
Answer: C
Question: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
A.30 Km/hr
B.36 Km/hr
C.80 Km/hr
D.90 Km/hr
Answer: B.36 Km/hr
Explanation: Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = x.
Then relative velocity = x+x = 2x
2x = distance/time = 240/12 = 20 m/s
Speed of each train = x = 20/2 = 10 m/s
= 10*18/5 km/hr = 36 km/hr
Option B
Question: The area of playground is 5700 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
A.a) $144
B.b) $150.50
C.c) $159.6
D.d) $158.60
Answer: C.c) $159.6
Explanation: total volume * unit cost = total cost
or, 5700 * 0.01 * 2.8 = total cost = 159.6=C
Question: A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.45
B.60
C.75
D.90
Answer: C.75
Explanation: Answer : C
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 400
16x = 400
x = 25.
Hence, total number of notes = 3x = 75.
Question: An design manager has 10patterns of chairs & 9patterns of tables. In how many ways can he make a pair of table & chair?
A.20
B.40
C.80
D.90
Answer: D.90
Explanation: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 9 ways
Hence one chair and one table can be arranged in 10 x 9 ways = 90 ways
D
Question: The perimeter of a square is 52 m. Find the area of the square.
A.161 m².
B.164 m².
C.166 m².
D.169 m².
Answer: D.169 m².
Explanation: Perimeter of square = 52 m
But perimeter of square = 4 × side
Therefore, 4 × side = 52 m
Therefore, side= 52/4 m = 13m
Now, the area of the square = (side × side)
Therefore, area of the square = 13 × 13 m² = 169 m².
ANSWER : OPTION D
Question: Find the distance covered by a man walking for 36min at a speed of 10km/hr?
A.1km
B.3km
C.6 km
D.5km
Answer: C.6 km
Explanation: Distance = 10*36/60 =6 km
Answer is C
Question: A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train?
A.90
B.60
C.120
D.180
Answer: A.90
Explanation: Length = Speed * time
Speed = L/T
S = 2500/100
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer:A
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
A.18
B.68
C.67
D.55
Answer: A.18
Explanation: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162
= 18
Answer:A
Question: Kail purchased n items from a catalog for $10 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?
A.11n + 2
B.11n + 4
C.11n + 3
D.9n + 3
Answer: C.11n + 3
Explanation: its C
n items for $10 each
total price $10n
postage and handling of $4 for 1st item and $1 for the rest
total postage and handling = $ [4+ (n-1)]
= $ n+3
total cost
10n+n+3 = 11n+3
Question: In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
A.A)136
B.B)627
C.C)153
D.D)721
Answer: A.A)136
Explanation: 46 + 28 + 10 = 84%
100 – 84 = 16%
850 * 16/100 = 136
Answer:A
Question: A tank can be filled by pipe A in 5 hours and by pipe B in 8 hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled?
A.2.6 hours
B.3.6 hours
C.4.6 hours
D.5.6 hours
Answer: B.3.6 hours
Explanation: Let's first find the rates of the pumps and the drainage hole
pump A: 1 / 5 , pump B: 1 / 8 , drainage hole: 1 / 20
Let t be the time for the pumps to fill the tank. The pumps ,add water into the tank however the drainage hole drains water out of the tank, hence
t ( 1 / 5 + 1 / 8 - 1 / 20) = 1
Solve for t
t = 3.6 hours
Answer B
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is
A.4/5
B.7/11
C.7/13
D.7/15
Answer: A.4/5
Explanation: Let the required fraction be x. Then	1	- x =	9
x	20
1 - x2	=	9
x	20
20 - 20x2 = 9x
20x2 + 9x - 20 = 0
20x2 + 25x - 16x - 20 = 0
5x(4x + 5) - 4(4x + 5) = 0
(4x + 5)(5x - 4) = 0
x =	4/5
A)
Question: A box contains 8 apples, 7 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: P(choosing a red apple 5 times in a row) = 7/8*6/7*5/6*4/5*3/4 = 3/8 < 0.5
The answer is C.
Question: When not moving on the sidewalk, Maya can walk the length of the sidewalk in 7 minutes. If she stands on the sidewalk as it moves, she can travel the length in 4 minutes. If Maya walks on the sidewalk as it moves, how many minutes will it take her to travel the same distance? Assume she always walks at the same speed, and express your answer as a decimal to the nearest tenth.
A.2.9
B.2.5
C.2.7
D.2.1
Answer: B.2.5
Explanation: Explanation:
Assume distance of sidewalk "x"
Speed 1 (moving on sidewalk)
Speed 2 (moving off sidewalk)
Since both the movements are in same direction, we can do speed 1 + speed 2
Speed 1 = x4x4
Speed 2 = x7x7
Speed 1 + speed 2 = 11x2811x28 = = 0.39286x
Now new time while moving on sidewalk = x0.39286xx0.39286x = 2.54544
Hence, the answer is 2.5
Answer: B
Question: There are 21 balls in a jar: 14 red, 4 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?
A.1/12
B.3/4
C.6/9
D.6/7
Answer: D.6/7
Explanation: Blue + Red =18
Total number of balls is 14+4+3=21
So the answer is 18/21=6/7
Answer D
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
A.109 ways
B.908 ways
C.128 ways
D.108 ways
Answer: D.108 ways
Explanation: The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer:D
Question: A shopkeeper sold an article at $1800 with 20% profit. Then find its cost price?
A.$1000
B.$1500
C.$1850
D.$1600
Answer: B.$1500
Explanation: cost price = selling price *100/(100+profit)
C.P. = 1800*100/120 = $1500
Answer is B
Question: For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution?
A.12
B.9
C.3
D.7.5
Answer: B.9
Explanation: we have 2 equations
1. 3(3x + 4y) = 36 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B