RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
A.91.5 cm
B.91.6 cm
C.91.2 cm
D.91.3 cm
Answer: A.91.5 cm
Explanation: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer: A
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for five years?
A.31500
B.27773
C.29989
D.28800
Answer: A.31500
Explanation: Simple interest = (18000 * 5 * 15)/100 = Rs. 13500
Amount = P + I = 18000 + 13500 = Rs. 31500
Answer: A
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 4914 Nis, how much more money does Nick contribute than Archi?
A.128 Nis
B.212 Nis
C.234 Nis
D.245 Nis
Answer: C.234 Nis
Explanation: E:N:A 5:3:2.5
so total = 5x + 3x + 2.5 x = 10.5 x = 4914
so x = 468
Nick Contribution is 0.5 more than Archi so 0.5 x =0.5 * 468 = 234
So C. 234 Nis is the correct answer
Question: The sum of ages of 5 children born 3 years different each is 50 yrs. What is the age of the Elder child?
A.7
B.9
C.16
D.18
Answer: C.16
Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
x+12= 4+12= 16
C
Question: A man can row downstream at 18 kmph and upstream at 12 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.3
B.5
C.6
D.4
Answer: A.3
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 12 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 3. Answer: A
Question: If r = 2^3 * 5^2 * 7 and s = 2^3 * 3^2 * 5, which of the following is equal to the greatest common divisor of r and s?
A.2 * 5
B.2^3 * 5
C.2^3 * 5^2
D.2*3*5*7
Answer: B.2^3 * 5
Explanation: GCD = product of prime factors raised to the least power = 2^3 * 5
The answer is B.
Question: In 10 years,A will be twice as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is :
A.19 Years
B.29 Years
C.39 Years
D.49 Years
Answer: C.39 Years
Explanation: Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
∴ (x + 9)+ 10 = 2 (x - 10) ⇔ x + 19 = 2x- 20 ⇔ x = 39.Answer C
Question: The H.C.F. and L.C.M. of 0.63, 1.05 and 2.1
A.(i)0.20(ii)6.31
B.(i)0.21(ii)5.30
C.(i)0.21(ii)6.30
D.(i)1.21(ii)6.50
Answer: C.(i)0.21(ii)6.30
Explanation: Explanation :
Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10.
Without decimal places, these numbers are 63, 105 and 210.
Now, H.C.F. of 63, 105 and 210 is 21.
H.C.F. of 0.63, 1.05 and 2.1 is 0.21.
L.C.M. of 63, 105 and 210 is 630.
L.C.M. of 0.63, 1.05 and 2.1 is 6.30.
ANSWER IS C
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 140 mph. On the way home, I flew 88 mph. What was my average speed for the trip?
A.114 mph
B.110 mph
C.88 mph
D.100 mph
Answer: A.114 mph
Explanation: (140 mph +88 mph)/2= 114 mph
Correct answer is: A
Question: Pradeep has to obtain 25% of the total marks to pass. He got 185 marks and failed by 25 marks. The maximum marks are
A.840
B.600
C.800
D.1000
Answer: A.840
Explanation: Explanation :
Let their maximum marks be x.
Then, 25% of x = 185 + 25
=>25/100x= 210
x = (210100/25)
x= 840.
Answer : A
Question: On what sum will the compound interest for 2 1⁄2 years at 10% amount to Rs. 31762.5?
A.Rs.5000
B.Rs.30000
C.Rs.25000
D.Rs.20000
Answer: C.Rs.25000
Explanation: Explanation:
P(1+10/100)2 × (1+(1/2×10)/100) = 31762.5
P(11/10)2 × (21/20) = 31762.5
P = (31762.5 × 20 × 10 × 10)/(21 × 11 × 11)
= (1512.5 × 20 × 10 × 10)/(11 × 11)
= (137.5 × 20 × 10 × 10)/11
= 12.5 × 20 × 10 × 10 = Rs. 25000
Answer: Option C
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
A.2.15 pm
B.2.15 am
C.3.15 pm
D.3.15 am
Answer: A.2.15 pm
Explanation: Suppose they meet x hours after 10 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Answer is A.
Question: 2 no's are respectively 40% & 60% more than 3rdnumber. Find the ration of two numbers ?
A.4 : 5
B.5 : 7
C.7 : 8
D.7 : 9
Answer: C.7 : 8
Explanation: Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B /5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.
C
Question: A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is:
A.122
B.210
C.216
D.217
Answer: C.216
Explanation: First step:
We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216
Answer: C.
Question: A single discount equivalent to the discount series of 10%, 10% and 5% is?
A.23.05
B.31.95
C.21.65
D.23.45
Answer: A.23.05
Explanation: 100*(90/100)*(90/100)*(95/100) = 76.95
100 - 76.95 = 23.05
Answer: A
Question: What is the value of n if the sum of the consecutive odd intergers W from 1 to n equals 169?
A.47
B.25
C.37
D.33
Answer: B.25
Explanation: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.
Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.
a=1 (first term)
d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2
*On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.
But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.
Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.
It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Question: The average age of the district level hockey team of eleven is 22 years.The average age gets increased by 1 year when the coach age is also included.what is the age of the coach ?
A.22 yrs
B.34 yrs
C.27 yrs
D.28 yrs
Answer: B.34 yrs
Explanation: Total age of players in team = 22 x 11 = 242
When coach is included, total members = 12, Avg age increases by one becomes 23
Total age when coach is included = 23x12 = 276
Age of coach = 276-242 = 34 yrs.
Answer: B
Question: An aircraft is flying at a height of 3000m from the ground at an average speed of 400 km/hr while descending. It has to travel 5 kms before it can touch down the runway and start operating its break system. It will take less than 10 seconds to reach the touch down point. How far it is from the touch down point if it had been on they ground.
A.5 kms
B.4 kms
C.3 kms
D.6 kms
Answer: B.4 kms
Explanation: answer is 4
simple Pythagoras theorem
ANSWER:B
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
A.3 1/9%
B.3 7/3%
C.7 1/3%
D.5 1/3%
Answer: A.3 1/9%
Explanation: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Question: How many three digit numbers can having only two consecutive digits identical is
A.153
B.162
C.168
D.163
Answer: B.162
Explanation: When 0 is the repeated digit like
100, 200, ...., 9 in number
When 0 occurs only once like
110, 220, ....., 9 in number
When 0 does not occur like
112,211, ....., 2 × (8 × 9) = 144 in number.
Hence, total = 9 + 9 + 144 = 162.
Answer B
Question: If m^2-8m+1=0,then m^3+m^(-3)= ?
A.487
B.488
C.489
D.457
Answer: B.488
Explanation: here from equation 1 we will get
m^2-8m+1=0
m^2=8m-1
m=(8m-1)/m.........(1)
m=8-1/m
so m+1/m=8
now in equation 2
m^3+1/m^3
(m+1/m)(m^2 - m*1/m + 1/m^2)
(m+1/m)(m^2 - 1 + 1/m^2)
(m+1/m)(m^2 + 1/m^2 - 1)
(m+1/m){(m+1/m)^2 - 2m*1/m - 1} {since a^2+b^2=(a+b)^2-2ab}
(m+1/m){(m+1/m)^2 - 2-1}
now putting the value of m from equation 1
8(8^2-2-1)
8(64-3)
=488
ANSWER:B
Question: The ratio of the radius of two circles is 2: 7, and then the ratio of their areas is?
A.1:7
B.2:9
C.1:9
D.4:49
Answer: D.4:49
Explanation: r1: r2 = 2: 7
Î r1^2: Î r2^2
r1^2: r2^2 = 4:49
Answer: D
Question: A girl was asked to multiply a certain number by 43. She multiplied it by 34 and got his answer less than the correct one by 1215. Find the number to be multiplied.
A.130
B.132
C.135
D.136
Answer: C.135
Explanation: Let the required number be x. Then,
43x – 34x = 1215 or 9x = 1215 or x = 135.
Required number = 135
ANSWER:C
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?
A.24
B.125
C.243
D.504
Answer: D.504
Explanation: P=3, R=4, and T=2.
There are following cases possible:
1. Different kinf of plays:
PRT (Any combination) = 3*4*2*3!=144.
2. Two same kind of plays and one from other kind of play:
PPR (Any combination. Notice that the two P's here must be different) = C23∗4∗3!=72C32∗4∗3!=72;
PPT = C23∗2∗3!=36;
RRP = C24∗3∗3!=108
RRT = C24∗2∗3!=72
TTP = C22∗3∗3!=18
TTR = C22∗4∗3!=24
3. All three plays are of the same kind:
PPP = C^3_3*3!=6
RRR = C^3_4*3!=24
TTT is not possible because we have only two T's.
Total = 144 + 72 + 36 + 108 + 72 + 18 + 24 + 6 + 24 = 504.
Answer: D.
Question: 3889 + 16.952 - ? = 3854.002
A.51.95
B.49.75
C.45.97
D.47.59
Answer: A.51.95
Explanation: Let 3889 + 16.952 - x = 3854.002.
Then x = (3889 + 16.952) - 3854.002
= 3905.952 - 3854.002
= 51.95.
Answer is A
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.299
B.180
C.288
D.127
Answer: B.180
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: B
Question: 8597 - ? = 7429 - 4358
A.5426
B.5706
C.5526
D.5476
Answer: C.5526
Explanation: Explanation:
7429 Let 8597 - x = 3071
-4358 Then, x = 8597 - 3071
---- = 5526
3071
----
Answer: C
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is
A.32 years
B.36 years
C.38 years
D.40 years
Answer: C.38 years
Explanation: Solution
Let Rajan's present age be x years. Then, his age at the time of marriage	=(x-8) years.
Therefore	x= 6/5(x-6)
5x = 6x-48
x=48.
Rajan's sister's age at the time of his marriage=(x-8)-10	=(x-18)=30
Rajan's sister's present age	=(30+8)
= 38 years.
Answer C
Question: Which of the following is closer to (20!+19!)/(20!-19!)?
A.11
B.13
C.1
D.3
Answer: C.1
Explanation: Notice that 20! = (20)(19!),
(20!+19!)*(20!-19!)=[19!(20+1)]*[19!(20-1)]
= 21/19
≈ 1
Answer: C
Question: Let X be the smallest positive integer such that 28 and 42 are factors of 678 - X, so the value of X is:
A.28
B.48
C.6
D.62
Answer: C.6
Explanation: You can simply check which of the possible values for X will make 678-X divisible by 28 and 42 simultaneously.
The only possible value is X = 6 (because 678 - 6 = 672 = 28*24 = 42*16).
Answer C
Question: If |8y−3|=|2y+7|, which of the following could be a value of y?
A.1
B.5/3
C.2/5
D.-2/3
Answer: B.5/3
Explanation: 8y − 3 = 2y + 7 or 8y − 3 = -2y - 7
6y = 10 or 10y = -4
y = 5/3 or y = -2/5
Answer: B
Question: A sum fetched total simple interest of 4016.25 at the rate of 10 p.c.p.a. in 5 years. What is the sum?
A.8925
B.8032.5
C.4462.5
D.8900
Answer: B.8032.5
Explanation: Let the sums be P.
Now, 50% of P = 4016.25
or, P = 8032.5
Answer B
Question: The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: Explanation:
P(1+20/100)n>2P =>(6/5)n>2.
Now,(6/5x6/5x6/5x6/5)>2.
So, n=4years.
ANSWER IS B
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is 3/4 empty, it is filled with brand X gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand X gasoline. At this time, what percent of the gasoline in the tank is brand Z?
A.41%
B.42%
C.43%
D.43.75%
Answer: D.43.75%
Explanation: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (3/4)*(1/2) + 1/2 = 7/8
4th step: brand Z is (1/2)*(7/8) = 7/16 = 43.75%
Answer (D)
Question: How many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers?
A.1200
B.1092
C.1082
D.1192
Answer: B.1092
Explanation: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
ANSWER:B
Question: Jane makes toy bears. When she works with an assistant, she makes 53 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
A.20%
B.70%
C.100%
D.180%
Answer: B.70%
Explanation: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears/hr ([40 bears * 1.53] / [40 hrs * .90]).
[(1.7 - 1)/1] * 100% = 70%
ANSWER:B
Question: Two sets of 7 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A.24
B.17
C.28
D.42
Answer: D.42
Explanation: A=(1,2,3,4,5,6,7), sum of this=28
B=(7,8,9,10,11,12,13), sum of this=70
The differenct between 70-28=42
Hence,42 is the answer i.e.D
Question: The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?
A.432 sq m
B.363 sq m
C.452 sq m
D.428 sq m
Answer: B.363 sq m
Explanation: 2(3x + x) = 88
l = 33 b = 11
lb = 33 * 11 = 363
ANSWER:B
Question: A Cuban cigar would cost 2 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
A.17.7$.
B.15.7$.
C.25.5$.
D.35$.
Answer: B.15.7$.
Explanation: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options C,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know A cannot be the answer.
Therefore B is the answer.
Question: If 5 and 8 are factors of 60n, what is the minimum value of n?
A. 2
B. 3
C. 7
D. 14
Answer: A. 2
Explanation: 60n/7*8 should be integer => 2*2*3*5*n/5*2*2*2 = 3*n/2 must be an integer
for this to be true n must multiple of 2, thus min of n = 2
hence A
Question: Find the average of first 40 natural numbers.
A.20.5
B.18
C.19.5
D.19
Answer: A.20.5
Explanation: Sum of first n natural numbers = n( n+1)/2
So, sum of first 40 natural numbers = 40*41/2 = 820
Required average =820/40 =20.5
ANSWER:A
Question: If an item that originally sold for o dollars was marked up by m percent and then discounted by n percent, which of the following expressions represents the final price of the item?
A.(10,000o + 100o(m – n) – mno)/10,000
B.(10,000o + 100o(n – m) – mno)/10,000
C.(100o(m – n) – mno)/10000
D.(100o(n – m) – mno)/10000
Answer: A.(10,000o + 100o(m – n) – mno)/10,000
Explanation: Assume o=100, m=10, n=10. So final price is 99. Now put these value each option. Only option A will give right answer.
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is?
A.Rs. 3900
B.Rs. 4900
C.Rs. 4980
D.Rs. 5000
Answer: A.Rs. 3900
Explanation: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y =	5	x.
2
15x + 2y = 4000
15x + 2 x	5	x = 4000
2
20x = 4000
x = 200.
So, y = 5	x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
A)
Question: A person want to give his money of $2700 to his 3 children A,B,C in the ratio 5:6:9. What is the A+C share?
A.$1890
B.$2002
C.$3500
D.$1500
Answer: A.$1890
Explanation: A's share = 2700*5/20 = $675
C's share = 2700*9/20 = $1215
A+D = $1890
Answer is A
Question: An article when sold at a gain of 5% yields Rs. 15 more than when sold at a loss of 5%. The cost price of the article is:
A.Rs. 200
B.Rs. 150
C.Rs. 80
D.Rs. 64
Answer: B.Rs. 150
Explanation: 10/100 × x = 15 ⇒ x=150
As the loss and profit both are earned on the cost price.
Answer: B
Question: In what time will a train 110 m long cross an electric pole, it its speed be 144 km/hr?
A.2.75 sec
B.4.25 sec
C.5 sec
D.12.5 sec
Answer: A.2.75 sec
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 110/40 = 2.75 sec.
ANSWER:A
Question: Simplify (212 * 212 + 312 * 312 )
A.132288
B.142088
C.142188
D.142288
Answer: D.142288
Explanation: Explanation:
Trick: Above equation can be solved by using following formula
(a2+b2)=1/2((a+b)2+(a−b)2)
Option D
Question: (3*10^2)*(4*10^-2)=?
A.14
B.12
C.1200
D.1.2
Answer: B.12
Explanation: 3*10^2=300
4*10^-2=0.04
(3*10^2)*(4*10^-2)=300*0.04=12.00
The answer is option B
Question: The combined salaries of three brothers is $45,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?
A. 10,000
B. 12,000
C. 15,000
D. 20,000
Answer: A. 10,000
Explanation: Mr. Small = x;
Mr. Middle = 3/2*x;
Mr. Big = 2x.
x + 3/2*x + 2x = 45 --> x=10
Answer: A
Question: The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 1988, the price of commodity X was 4.20 and that of Y was 6.30, in which year will commodity X cost 40 paise more than commodity Y?
A.1997
B.1998
C.1999
D.2000
Answer: B.1998
Explanation: Suppose in ‘n’ years the price of comodity X will be more by 40 paise than that of commodity Y.
∴ 420 + 40n – 630 – 15n = 40
or, 25n – 210 = 40
or, 25n = 250
or, n = 250⁄25 = 10 years.
Answer B
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
A.13.1 sec
B.12.1 second
C.22.1 sec
D.32.1 sec
Answer: B.12.1 second
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Question: A certain team consists of 5 professors and 4 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
A.74
B.80
C.86
D.92
Answer: B.80
Explanation: The total number of ways to form a group of 3 from 9 people is 9C3 = 84
The number of ways to form a group without a professor is 4C3 = 4
The total number of ways to form a valid group is 84 - 4 = 80.
The answer is B.
Question: Which of the following could be the sum of the reciprocals of two different prime numbers?
A.7/13
B.10/12
C.11/30
D.23/50
Answer: B.10/12
Explanation: Here, the condition is that there should be two different prime nos.
A 13 = 13 x 1 ( 1 is not a prime number)
B 21 = 7 x 3 ( both 7 and 3 are prime nos)
C 30 = 10 * 3 or 5* 6 ( It can be written both ways, but 10 and 6 are not prime nos)
D 50 = 10 * 5 ( 10 is not a prime number)
E 77 = 11 * 7 ( both are prime numbers)
Options A, C, D are eliminated.
We are left with options B and E.
1/11 + 1/7 = 18/77 and not 19/77. Hence this option is eliminated.
Option B is the correct
Question: A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 200 square feet, what is the total length of the fence, in feet?
A.10
B.20
C.30
D.40
Answer: D.40
Explanation: two sides EACH = x the third = 2x and the wall length is thus 2x too
x*2x = 2x^2 = 200 ie x^2 = 100 ie x = 10
L = 20 W=10
TOTAL LENGHT OF FENCE = 2*10 + 20 = 40
MY ANSWER IS D
Question: The price of rice is reduced by 2%. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier?
A.48 kg
B.49 kg
C.50 kg
D.51 kg
Answer: C.50 kg
Explanation: Sol.
Let the original price be Rs. 100 per kg.
Money required to buy 49 kg of rice = Rs. (100 x 49) = Rs. 4900.
New price = Rs. 98 per kg.
∴ Quantity of rice bought = [4900 / 98] kg = 50 kg.
Answer C
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?
A.9 min
B.8 min
C.4 min
D.6 min
Answer: B.8 min
Explanation: Explanation:
Tank can be filled by pipe A in 12 minutes and pipe B in 24minutes.
=> Part filled by A in 1 minute= 1/12
=> Part filled by B in 1 minute= 1/24
=> Part filled by both in 1 minute= 1/12 + 1/24
= 3/24=1/8
Time taken to fill the entire tank = 8 minutes
ANSWER B
Question: H.C.F of 4 * 27 * 3125, 8 * 9 * 25 * 7 and 16 * 81 * 5 * 11 * 49 is:
A.240
B.790
C.840
D.180
Answer: D.180
Explanation: Explanation:
4 * 27 * 3125 = 2^2 * 3^3 * 5^5;
8 * 9 * 25 * 7 = 2^3 * 3^2 * 5^2 * 7;
16 * 81 * 5 * 11 * 49 = 2^4 * 3^4 * 5 * 7^2 * 11
H.C.F = 2^2 * 3^2 * 5 = 180.
Answer: Option D
Question: A train sets off at 2:00 pm at the speed of 70 km/h. Another train starts at 3:00 pm in the same direction at the rate of 80 km/h. At what time will the second train catch the first train?
A.10:00
B.10:30
C.11:00
D.11:30
Answer: A.10:00
Explanation: In one hour the first train travels 70 km.
The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.
The second train will catch the first train in 70/10 = 7 hours, so at 10:00 pm.
The answer is A.