RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
A.16500
B.17568
C.17576
D.13454
Answer: C.17576
Explanation: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
A.150 meter
B.299 meter
C.278 meter
D.208 meter
Answer: A.150 meter
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
= 150 meter
Answer:A
Question: If the sum of n consecutive positive integers is 33, what of the following could be the value of n?
I. 3
II. 6
III. 11
A.I only
B.II only
C.III only
D.I and II
Answer: D.I and II
Explanation: solved it the way bunuel explained, although took some time to arrive to the answer choice.
3 -> 10+11+12=33.
6 ->3+4+5+6+7+8=33.
11 -> since we are told that we have a set of n consecutive POSITIVE numbers, we can have the smallest possible numbers:
1+2+3+4+5+6+7+8+9+10+11 - the sum is way over 33, it is actually 11*12/2 = 11*6=66.
thus, only I and II works. the answer is D
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
A.22
B.99
C.24
D.77
Answer: C.24
Explanation: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph.Answer: C
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
A.12
B.15
C.14
D.18
Answer: C.14
Explanation: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
ANSWER C
Question: A certain school principal must choose 5 students to attend a field trip out of a group of 10 students. In addition, out of the 5 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 5 students and then select the treasurer and the note-taker?
A.1,260
B.2,520
C.5,040
D.6,020
Answer: C.5,040
Explanation: Out of 10 students, 5 students can be chosen in 10C5 ways.
Out of the 5 chosen students, note taker role can be taken in 5 ways
Since the note taker role is already taken by 1 student, the treasure role can be taken in 4 ways
Total number of ways = 10C5 * 5 * 4 = 5040
Answer: C
Question: What is the remainder when 3990990900032 is divided by 32 ?
A.0
B.8
C.4
D.2
Answer: A.0
Explanation: Though i was unaware of the divisibility test for 32 but i guessed the pattern!!
divisibility rule for 4- last two digits must be divisible by 4
divisibility rule for 8- last three digits must be divisible by 8
similarly, divisibility rule for 32 - last five digits must be divisible by 32
Hence, Ans A
Question: From the below series find the remainder?
1201 × 1203 ×1205 × 1207 is divided by 6
A.3
B.6
C.8
D.4
Answer: A.3
Explanation: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
A.8
B.6
C.9
D.3
Answer: B.6
Explanation: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 30%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
A.100
B.125
C.122.2
D.105.5
Answer: C.122.2
Explanation: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 30%, therefore bringing down the price to $45.
4) Now 67.5 has to be added byX %in order to equal the original price.
45 + ( X% ) 45 = 100.
Solving this eq for X, we get X = 122.2
Ans is C.
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $38. If $2,000 is the total amount invested, how much is invested at 8 percent?
A.$700
B.$800
C.$900
D.$1100
Answer: C.$900
Explanation: 0.1x = 0.08(2000-x)+38
0.18x = 198
x = 1100
Then the amount invested at 8% is $2000 - $1100 = $900
The answer is C.
Question: a is a positive integer and multiple of 2; p = 4^a, what is the remainder when p is divided by 10?
A.10
B.6
C.4
D.0
Answer: B.6
Explanation: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the a is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, a must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since a must be an even integer, the units digit of p=4^a will always be 6. Consequently, the remainder when p=4^a is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
a=2 --> p=4^a=16 --> p/10 = 1 with a remainder of 6
a=4 --> p=4^a=256 --> p/10 = 25 with a remainder of 6
a=6 --> p=4^a=4096 --> p/10 = 409 with a remainder of 6
a=8 --> p=4^a=65536 --> p/10 = 6553 with a remainder of 6
Answer: B.
Question: A room 8 m 47 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
A.13636
B.13440
C.13647
D.13431
Answer: D.13431
Explanation: Explanation:
Area of the room = (847 x 777) cm2.
Size of largest square tile = H.C.F. of 847 cm and 777 cm = 7 cm.
Area of 1 tile = (7 x 7) cm2.
Number of tiles required =(847×777)/(7×7)=13431
Answer: Option D
Question: If n is the product of 3 consecutive integers, which of the following must be true about n?
I. n is a multiple of 2
II. n is a multiple of 3
III. n is a multiple of 4
A.I only
B.II only
C.III only
D.I and II
Answer: D.I and II
Explanation: n is the product of 3 consecutive integers.
So, according to the rule, n must be divisible by 3, 2 and 1
So, we already know that statements I and II must be true.
Do we need to check statement III? No.
Notice that NONE of the answer choices include all 3 statements. Since we've already concluded that statements I and II are true, the correct answer is D.
Question: 36 men can complete a piece of work in 18 days. In how many days will 72 men complete the same work ?
A.24
B.17
C.18
D.9
Answer: D.9
Explanation: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
72 : 36 :: 18 : x
x = 9
Answer: D) 9 days
Question: If x is a positive integer, which of the following must be odd?
A.x+1
B.x^2+x
C.x^2+x+7
D.x^2−1
Answer: C.x^2+x+7
Explanation: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 7 = ODD
Hence C.
Question: The length of the bridge, which a train 110 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.265
B.288
C.245
D.776
Answer: A.265
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (110 + X)/30 = 25/2 ==> 2(110 + X) = 750 ==> X
= 265 m.
Answer:A
Question: A bag contains 8 red, 6 blue and 4 green balls. If 2 ballsare picked at random, what is the probability that both are red?
A.1/13
B.2/23
C.5/26
D.7/30
Answer: D.7/30
Explanation: P(Both are red),
=8C216C2=8C216C2
=28/120=7/30
D
Question: A train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds.The speed of the second train is
A.60 kmph
B.66 kmph
C.72 kmph
D.99 kmph
Answer: D.99 kmph
Explanation: Given that two trains are of same length i.e..150 mtrs
first train passes the km stone in 15 seconds. here we have time and distance so speed=150/15=10 m/s
we need to find out the second train speed.
suppose the speed of the 2nd train is x m/s
Relative speed of two trains is (10+x)
==> (150+150)/(10+x)=8
==> (300)/(10+x)=8
==> 300=80+8x
==> 300-80=8x
==> 220=8x
:- x=55/2 m/s
convert m/s into km/ph
(55/2)*(18/5)=99kmph
ANSWER:D
Question: A committee has 4 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
A.120
B.160
C.200
D.240
Answer: A.120
Explanation: The number of ways to select two men and three women = 4C2 * 6C3 = 6 * 20 = 120
The answer is A.
Question: The sides of a cube are in the ratio of 1:2 the ratio of their volumes is ?
A.1:2
B.1:4
C.1:8
D.2:1
Answer: C.1:8
Explanation: 1:8Answer : C
Question: A alone can do a work in 12 days. A and B together finished work and got rs.54 and rs.18 respectively. In how many days was the work finished?
A.12
B.14
C.9
D.10
Answer: C.9
Explanation: A does the work in 12 days
and A and B together finished work and got rs.54 and rs.18 respectively
so B will do work in 12*3 = 36 days (because he got 1/3 money relative to other)
so one day work = 1/12 + 1/36 = 4/36 = 1/9
so total days required = 9
ANSWER:C
Question: A batsman scored 130 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
A.45(4/11) %
B.45 %
C.53(11/13) %
D.44(5/11) %
Answer: C.53(11/13) %
Explanation: Explanation :
Total runs scored = 130
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 130 - 60 = 70
Required % = (70/130) × 100 = 700/13 = 53(11/13)%
Answer : Option C
Question: The L.C.M of two numbers is 48. The numbers are in the ratio 4:3. The sum of numbers is:
A.28
B.30
C.40
D.50
Answer: A.28
Explanation: Let the numbers be 4x and 3x.
Then, their L.C.M = 12x. So, 12x = 48 or x = 4.
The numbers are 16 and 12.
Hence, required sum = (16 + 12) = 28.
ANSWER:A
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
A.150
B.190
C.100
D.240
Answer: D.240
Explanation: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is x+2x=3x This must be equal to 360.
3x=360
x=360/3
x=120
Therefore, the salesman sold 120 kg in the morning and 2⋅120=240 kg in the afternoon.
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 8 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
A.61
B.62
C.65
D.63
Answer: D.63
Explanation: Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:
Assuming x motorcycles were sold every month initially.
(568000/x + 1000)(x-8) = 594000
(568/x + 1)(x-8) = 594
Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 8 = 63 bikes this month
Answer (D)
Question: Convert the following unit:
2.5 hectares in ares
A.200 ares.
B.210 ares.
C.220 ares.
D.250 ares.
Answer: D.250 ares.
Explanation: 2.5 hectares in ares
1 hectare = 100 ares
Therefore, 2.5 hectares = 2.5 × 100 ares
= 250 ares.
ANSWER : OPTION D
Question: A teacher will pick a group of 4 students from a group of 9 students that includes Bart Lisa and john. If one of all the possible four-student groups is picked at random, what is the probability of picking a group that includes john Bart and Lisa?
A.1/7
B.3/14
C.1/4
D.1/21
Answer: D.1/21
Explanation: Probability = Favorable Outcomes / Total Outcomes
Total Outcomes= Total No. of ways of Picking Group of 4 out of 9 = 9C4 = 9! / (5! * 4!) = 126
Favorable Outcomes= Total No. of ways of Picking Group of 4 out of 9 such that J, B and L are always in the group (i.e. we only have to pick remaining one out of remaining 6 as J, B and L must be there is group) = 6C1 = 6
Hence,Probability=6/126=1/21
Answer: Option D
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
A.62.5
B.62.7
C.62.9
D.62.1
Answer: A.62.5
Explanation: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Question: Which of the following must be an integer if the integer x is divisible by both 15 and 21?
A.x/252
B.x/189
C.x/126
D.x/105
Answer: D.x/105
Explanation: the integer has to be multiple of LCM of 15 and 21, which is 105..
so x/105 will be an integer
ans D
Question: If you cut a 20ft piece of wood into two pieces making one piece 6ft longer than the other. What size is the smaller piece?
A.4ft
B.7ft
C.8ft
D.10ft
Answer: B.7ft
Explanation: Total length is 20ft, one piece is 6ft longer (x+6), leaving the other piece to figure out (x).
(x)+ (x+4)=20
x+x+6-6=20-6
2x=14
2x/2=14/2
x=7
The piece is B) 7ft.
Question: If 2a = 3b and ab ≠0, what is the ratio of a/3 to b/2?
A.27/8
B.8/27
C.1
D.9/4
Answer: C.1
Explanation: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 2a = 3b
Here's one pair: a =3 and b =2
What is the ratio of a/3 to b/3?
In other words, what is the value of (a/3)/(b/2)?
Plug in values to get: (a/3)/(b/2) = (3/3)/(2/2)
= 1/1
= 1
C
Question: If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is?
A.2:1
B.2:7
C.2:2
D.2:6
Answer: A.2:1
Explanation: Let 1 man's 1 day work = x and 1 boy's 1 day work = y.
Then, 12x + 16y = 1/5 and 13x + 24y = 1/4
Solving these two equations, we get:
x = 1/100 and y = 1/200
Required ratio = x:y = 1/100 : 1/200 = 2:1.
Answer:A
Question: What number should replace the question mark?
105, 87, 70, 52, 35,?
A.49
B.37
C.70
D.17
Answer: D.17
Explanation: D
17
The sequence progresses -18, -17, -18, -17.
Question: A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ?
A.650 meter
B.555 meter
C.500 meter
D.458 meter
Answer: C.500 meter
Explanation: Explanation:
Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
=>800+x=65/3∗60
=>800+x=20∗65=1300
=>x=1300−800=500
So the length of the tunnel is 500 meters.
Option C
Question: In how many different ways can 3 identical green boots and 3 identical red boots be distributed among 6 people such that each person receives a pair of boots?
A.7209
B.4059659
C.2169
D.20
Answer: D.20
Explanation: How to solve:
1st Person: 6 has options
2nd Person: 5 has options…
Therefore, for all people: 6 x 5 x 4 x 3 x 2 = 720 arrangements.
Since the reds are identical, we divide by 3! Since the greens are identical, we divide by another 3!
So: in all, 720/[ 3! X 3! ] = 20 ways.
(e.g. Answer: D)
Question: How long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 200 m in length?
A.18.6 sec
B.14.9 sec
C.12.4 sec
D.16.8 sec
Answer: A.18.6 sec
Explanation: A
18.6 sec
D = 110 + 200 = 310 m
S = 60 * 5/18 = 50/3
T = 310 * 3/50 = 18.6 sec
Answer is A
Question: 8 is 6% of a, and 6 is 8% of b. c equals b/a. What is the value of c?
A.3/8
B.8/15
C.9/16
D.12/25
Answer: C.9/16
Explanation: 6a/100 = 8
a = 400/3
8b/100 = 6
b = 75
c = b/a = 75*3/ 400 = 9/16
The answer is C.
Question: In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 6 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?
A.d = p/1.06 - 0.18
B.d= (p-0.18)/1.06
C.d = (p-0.06)/1.18
D.d = p-0.24
Answer: B.d= (p-0.18)/1.06
Explanation: Let dealers price (d) be 1. so adding 6% to dealers price is d+ 6% of d. i.e. 1 + 6% of 1 which is1 + 0.06. then add 0.18 to the value.
Now 1.06 + 0.18. this is now 1.24. you have the gasoline stations price (p) as 1.24 dollars.
Now sub 1.24 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.
PS: always remember to start from E upwards.
Answer : B
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
A.42 6/8%
B.42 8/7%
C.72 6/7%
D.42 6/7%
Answer: D.42 6/7%
Explanation: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Question: If the product of the integers from 1 to n is divisible by 1029, what is the least possible value of n?
A.7
B.14
C.21
D.28
Answer: C.21
Explanation: 1029 = 7 x 7 x 7 x 3
N must include at least 7, 2*7, and 3*7.
The answer is C.
Question: If b, x, y, and z are positive integers and (x)×(y)×(z)=b^2, which of the following could be the values of x, y, and z?
A.3, 16, 25
B.9, 25, 24
C.2, 81, 32
D.2, 9, 16
Answer: C.2, 81, 32
Explanation: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*81*32 = 2*9*9*8*4 = 9*9*8*8
ans C
Question: A certain store sells all maps at one price and all books at another price. On Monday the store sold 9 maps and 6 books for a total of $20.00, and on Tuesday the store sold 9 maps and 8 books for a total of $30.00. At this store, how much less does a map sell for than a book?
A. $0.25
B. $0.50
C. $0.75
D. $3.9
Answer: D. $3.9
Explanation: 9x+6y=20
9x+8y=30
subtracting 1 from 2
-2y=-10
y=5
therefore
x=1.1
difference in price =3.9
D
Question: The compound interest on Rs.2,000 at 10% per annum for 3 years payable half yearly is
A.Rs.600
B.Rs.630
C.Rs.660
D.Rs.680
Answer: D.Rs.680
Explanation: amt=2000(1+r/2/100)^2n formulae as it is half yearlly
amt=2000(1+1/20)^4
amt=2680.19
ci= 2680.19-2000 = 680.00
ANSWER:D
Question: A boat can move upstream at 35 kmph and downstream at 65 kmph, then the speed of the current is?
A.15
B.8
C.9
D.12
Answer: A.15
Explanation: US = 35
DS = 65
M = (65- 35)/2
= 15
Answer:A
Question: Find the missing number in the given sequence : 1,4,7,?,13,16,?
A.10 & 19
B.8 & 17
C.9 & 18
D.11 & 20
Answer: A.10 & 19
Explanation: 1+3=4
4+3=7
7+3=10
10+3=13
13+3=16
16+3=19
ANSWER:A
Question: In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 4 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
A.3
B.6
C.8
D.9
Answer: B.6
Explanation: the choices give away the answer..
36 machines take 4 hours to fill 4 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 4*48/72*12/4 = 6
Ans B
Question: N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to N?
A.1 1/2
B.1 1/3
C.5/3
D.3/2
Answer: B.1 1/3
Explanation: "N is such that when multiplied by 0.75 gives 1" is written mathematically as
N * 0.75 = 1
Solve for N
N = 1/0.75 = 100/75 = (75 + 25) / 75 = 75/75 + 25/75 = 1+1/3
correct answer B
Question: A cylinder of height h is 8/9 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
A.25%
B.50%
C.68%
D.80%
Answer: C.68%
Explanation: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 8/9
New cylinder 3/5
So 3/5/8/9 = 3/5 * 9/8 = 12/15 = 4/5 = 0.680 or 68%.
Answer C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.10 m
B.16 m
C.245 m
D.19 m
Answer: C.245 m
Explanation: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x) = 750 => x
= 245 m.
Answer: C
Question: At a certain health club, 30 percent of the members use both the pool and sauna, but 35 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
A.33 1/3%
B.51 23/27%
C.50%
D.62 1/2%
Answer: B.51 23/27%
Explanation: P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
35% of (70-x) = x => 24.5 - 0.35x = x => x = 18 4/27% so only P = 70 -x = 51 23/27%
Answer B
Question: 15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
A.14
B.18
C.24
D.28
Answer: B.18
Explanation: Binders Books Days
15 1400 21
x 1600 20
x/15 = (1600/1400) * (21/20) => x = 18
ANSWER:B
Question: The difference between a two-digit number and the number after interchanging the position of the two digits is 54. What is the difference between the two digits of the number?
A.4
B.6
C.3
D.Cannot be determined
Answer: B.6
Explanation: Let the two-digit no. be l0x + y.
Then, (10x + y) â€“ (10y + x) = 36
or, 9(x â€“ y) = 54
or, x â€“ y = 6
Answer B
Question: On dividing number by 357, we get 39 as remainder. On dividing the same number by 17, what will be the remainder?
A.0
B.3
C.5
D.11
Answer: C.5
Explanation: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x = 5k + 3
x2 = (5k + 3)2 = (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder.
ANSWER:C
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
A.24
B.73
C.26
D.82
Answer: A.24
Explanation: Explanation:
Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2x2 + 26x - 140 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.
Answer: A
Question: A box contains 4 red chips and 3 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?
A.1/2
B.12/21
C.7/12
D.2/3
Answer: B.12/21
Explanation: Total selection ways: 7C2=7!/3!4!=21
Selecting one blue chip out of two: 3C1=3!/2!1!=3
Selecting one red chip out of four: 4C1=4!/1!3!=4
Thus, (3C1*4C1)/7C2=(3*4)/21=12/21=B