divelab/Sys2Bench huggingface dataset:
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
Options:
A)15 hours
B)20 hours
C)25hours
D)28 hours
E)18 hours
Rationale: Let the first pipe alone can fill the tank in x hours
Then the second pipe can fill the tank in (x-5) hours
and the third pipe can fill the tank in (x-5)-4 = (x-9) hours
part filled by first pipe and second pipe together in 1 hr = part filled by third pipe in 1 hr
(1/x)+1/(x−5)=1/(x−9)
(x−5)(x−9)+x(x−9)=x(x−5)
x^2−14x+45+x^2−9x=x^2−5x
−14x+45+x^2−9x=−5x
x^2−18x+45=0
(x−15)(x−3)=0
x=15 or 3
We can not take the value of x = 3 because, (x-9) becomes negative which is not possible
because the third pipe can fill the tank in (x-9) hours
Hence, x = 15
Answer is A
Answer: A
Question: You collect baseball cards. Suppose you start out with 15. Since her father makes baseball cards, Cindy decides to quadruple your baseball cards. Since you're nice, you give Mike 10 baseball cards. Tiffany gives you another 12 baseball cards. Pearl gives you another 23 baseball cards. How many baseball cards do you have at the end?
Options:
A)55
B)65
C)75
D)95
E)85
Rationale: Solution
Start with 15 baseball cards.
Cindy quadruples the number of baseball cards you have: 15 × 4 = 60 baseball cards.
Mike takes 10 baseball cards from you: 60 - 10 = 50 baseball cards.
Tiffany gives you 12 baseball cards: 50 + 12 = 62 baseball cards.
Pearl gives you 23 baseball cards: 62 + 23 = 85 baseball cards.
So you have 85 at the end.
Correct answer : E
Answer: E
Question: It costs a man 75 dollars to buy the things that he needs to make hotdogs. The city allows him to sell his hotdog somewhere near the city hall. However, the city hall charges him 1 dollar for each hotdog sold
Calculate the break even point if the price he charges for 1 hotdog is $1.50
Options:
A)140
B)150
C)160
D)170
E)180
Rationale: Let x be the number of hotdogs sold
Let C be the cost of buying and selling x hotdogs
Let R be the revenue made for selling x hotdogs
R = selling price of 1 hotdog × number of hotdogs sold
R = 1.50x
C = fixed cost + variable cost
variable cost = fee charged for 1 hotdog × number of hotdogs sold
variable cost = 1x
C = 75 + 1x
R = C
1.50x = 75 + 1x
1.50x - 1x = 75 + 1x - 1x
0.5x = 75
x = 150 since 0.5 × 150 = 75
The break even point is to sell 150 hotdogs.
Answer B
Answer: B
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)3
B)5
C)4
D)6
E)7
Rationale: T = 60/36 * 18/5 = 6 sec
Answer:D
Answer: D
Question: A contractor is engaged for 30days on the condition that he receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.490 in all. For how many days was he absent?
Options:
A)8
B)10
C)15
D)17
E)19
Rationale: 30 * 25 = 750
490
-----------
260
25 + 7.50 = 32.5
260/32.5 = 8
A
Answer: A
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+8)(2x-5) = 0?
Options:
A)1/12
B)1/6
C)1/4
D)1/3
E)1/2
Rationale: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5,x=-8 and x=5/2=2.5. So, one solutions present in our set of 12 distinct numbers, therefore P=1/12
Answer: A.
Answer: A
Question: The average score of a cricketer for seven matches is 56 runs. If the average for first four matches is 46, then average for last three matches is
Options:
A)33.25
B)32.25
C)65
D)67
E)69
Rationale: Explanation:
=(56×7)−(46×4)/3
=(392−184)/3=69
Answer: Option E
Answer: E
Question: Find the arithmetic mean L of all roots of the following equation- see an attachment.
Options:
A)2
B)1
C)0.5
D)-1/3
E)0.3
Rationale: arithmetic mean L your answer C and E are same, can you correct one of them please. thanks.C
Answer: C
Question: If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?
Options:
A)48
B)60
C)54
D)90
E)100
Rationale: Explanation:
When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60 * 64 * 150) / (80 * 80) = 90
Therefore, in a game of 150, R can give 60 points to Q.
ANSWER B
Answer: B
Question: Find: S.l. on Rs 3000 at 18% per annum for the period from 4th
Options:
A)118
B)105
C)108
D)110
E)111
Rationale: Explanation:
(24 + 31 + 18) days = 73 days = 1/5 year .
P = Rs 3000 and R = 18 % p.a.
S.I=(3000 *18 * 1/5)/100
ANSWER IS C
Answer: C
Question: In how much time will interest on Rs. 2300 at 4 1/2 percent p/a be Rs.310.50
Options:
A)5years
B)2years
C)4years
D)3 years
E)2 1/2 years
Rationale: 310 = (2300*T*9/2)/100
T = (310.50x100x2)/(300x9)= 3 years.
Answer: D
Answer: D
Question: What will be the fraction of 8%
Options:
A)1/20
B)1/50
C)1/75
D)2/25
E)None of these
Rationale: Explanation:
8*1/100 = 2/25.
Option D
Answer: D
Question: Two boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
Options:
A)A)4^30
B)B)2^30
C)C)1^30
D)D)3^30
E)E)6^30
Rationale: Each Mango can be given to any one of the two people or in other words..30 mango can be divided into 2 ways...so all 30 can be divided in 2^30 ways
ANS:B
Answer: B
Question: Compound interest earned on a sum for the second and the third years are Rs.12500 and Rs.14000 respectively. Find the rate of interest?
Options:
A)18% p.a.
B)22% p.a.
C)20% p.a.
D)12% p.a.
E)None of these.
Rationale: Rs.14000 - 12500 = Rs.1500 is the interest on Rs.12500 for one year.
Rate of interest = (1500/12500) * 100 = 12% p.a
ANSWER:D
Answer: D
Question: A bag contains six white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Options:
A)15/8
B)8/15
C)5/6
D)5/3
E)5/1
Rationale: Two balls can be picked from ten balls in 10Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (6 * 4) = 24/45 = 8/15
Answer: B
Answer: B
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/7 of the remaining paint. How many gallons of paint has Joe used?
Options:
A)18
B)128
C)175
D)216
E)250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/7)*270 = 38 gallons
Total paint used = 128 gallons.
Option B
Answer: B
Question: Let d > c > b > q. If c is twice as far from q as it is from d, and b is twice as far from c as it is from q, then (d - b)/(d - q) = ?
Options:
A)2/9
B)1/3
C)2/3
D)7/9
E)3/2
Rationale: Draw a number line and label with x and y. You would have:
Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y.
Now you can calculate d -b and d -a
d - b= x +2y = 7/2 y
d - q = x + 2x = 3x = 9/2y
Dividing both you get: 7/9
Answer D
Answer: D
Question: The ratio of two numbers is 2/3, and if a 1 is subtracted from the numerator and a 1 is added to the remainder the ratio becomes 1/2, then the numbers are.
Options:
A)6 and 9
B)6 and 10
C)6 and 8
D)6 and 7
E)6 and 11
Rationale: a:b=2:3 b=3/2a
a-1/b+1=1/2
solving this we get a=6 and b=9
ANSWER:A
Answer: A
Question: A jar full of whiskey contains 40% alcohol. A part of
this whiskey is replaced by another containing 19% alcohol
and now the percentage of alcohol was found to be 26%.
The quantity of whiskey replaced is?
Options:
A)2/3
B)1/3
C)1/4
D)1/2
E)1/5
Rationale: Strength of first jar 40% Strength of 2nd jar 19%
Mean Strength 26%
7 14
So,ratio of 1st and 2nd quantities =7:14 =1:2
Therefore required quantity replaced =2/3.
ANSWER A
Answer: A
Question: Which 2 digit number has its digits reversed when you double it and take 1?
Options:
A)33
B)34
C)35
D)36
E)37
Rationale: reverse it and you get 73 which is 2*37-1.
ANSWER:E
Answer: E
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 21 years. The ratio of their ages after 8 years will be
Options:
A)2 : 3
B)20 : 17
C)5 : 4
D)3 : 5
E)6 : 11
Rationale: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 21
x = 3
Mini’s age = 12 years
And Minakshi’s age = 9 years
Ratio of their ages after 8 years = (12 + 8) : (9 + 8) = 20 : 17
ANSWER:B
Answer: B
Question: A goods train runs at the speed of 72 km/hr and crosses a 290 m long platform in 26 sec. What is the length of the goods train?
Options:
A)278
B)166
C)151
D)230
E)109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 290)/26 = 20
x = 230 m.
Answer:D
Answer: D
Question: Find the difference between C.I and S.I on a sum of money Rs. 2000 for 2 years. at 4% p.a
Options:
A)Rs.2.20
B)Rs.3.20
C)Rs.4.20
D)Rs.5.20
E)Rs.3.25
Rationale: P9r/100)^2 =2000(4/100)^2 =Rs.3.20 Answer : B
Answer: B
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.55 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
Options:
A)7%
B)10%
C)11%
D)12%
E)15%
Rationale: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.
3(0.22-x)(15) + 2x(18) = 8.55
9.9 - 45x + 36x = 8.55
9x = 1.35
x = 0.15
The answer is E.
Answer: E
Question: (786×74) ÷ ? = 4847
Options:
A)A)4.8
B)B)12
C)C)58
D)D)68
E)E)48
Rationale: Explanation:
58164/x = 4847 => x = 58164/4847 = 12
Answer: Option B
Answer: B
Question: How many odd numbers between 10 and 2000 are the squares of integers?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: The numbers are the squares of 5, 7, 9,...,43 which includes 20 numbers.
The answer is E.
Answer: E
Question: If x^2−2ax+a^2=0 get value of x/a
Options:
A)1
B)2
C)3
D)4
E)7
Rationale: a is obviously non-zero. We divide the equation by
a^2
we get (x/a-1)^2=0
x/a=1
ANSWER A 1
Answer: A
Question: If 75 percent of a class answered the first question on a certain test correctly, 70 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Options:
A) 10%
B)(8) 20%
C) 30%
D) 50%
E) 65%
Rationale: {Total} = {First} + {Second} - {Both} + {Neither}
100% = 75% + 70% - {Both} + 20% --> {Both} = 65%.
Answer: E.
Answer: E
Question: If (a-5)(b-2) =0, which of the following must be true ?
I. a=5 and b=2
II. if a is not 5, then b=2
III. if a=5, then b is not=2
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: (a-5)(b-2)=0
So either a=5 or b=2 or both. It is 'or' not 'and', so it could be any of the three possibilities. Thus I and III are not necessarily true.
The answer is B.
Answer: B
Question: If the compound interest on a certain sum of money for 5 years at 10% per annum be Rs. 993, what would be the simple interest?
Options:
A)Rs. 1500
B)Rs. 890
C)Rs. 895
D)Rs. 900
E)None
Rationale: Let P = Principal
A - Amount
We have a = P(1 + R/100)3 and CI = A - P
ATQ 993 = P(1 + R/100)3 - P
? P = 3000/-
Now SI @ 10% on 3000/- for 5 yrs = (3000 x 10 x 5)/100
= 1500/-
Answer: A.
Answer: A
Question: 10 camels cost as much as 24 horses, 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants. If the cost of 10 elephants is Rs.150000, find the cost of a camel?
Options:
A)s.9800
B)s.3800
C)s.9800
D)s.6000
E)s.6880
Rationale: Cost of the camel = P
10 camels = 24 horses
16 horses = 4 oxen
6 oxen = 4 elephants
10 elephants = Rs.150000
P = Rs.[(24 * 4 * 4 * 150000)/(10 * 16 * 6 * 10)]
P = Rs.(57600000/9600) => P = Rs.6000
Answer:D
Answer: D
Question: √{(6.3)(10^9)} is closest to which of the following?
Options:
A)1,500
B)6,000
C)25,000
D)80,000
E)150,000
Rationale: √{(6.3)(10^9)} = √{(63)(10^8)} = √(63)√(10^8) = (√63) * 10,000 which is almost 80,000.
The answer is D.
Answer: D
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 30% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
Options:
A)35.67%
B)64.75%
C)68.57%
D)69.10%
E)none of these
Rationale: Girls = 900, Boys = 1100
Passed = ( 30% of 1100 ) + ( 32% of 900)
= 330 + 288 = 618
Failed = 2000 - 618 = 1382
Failed % = [(1382/2000) x 100]%
= 69.1%.
ANSWER:D
Answer: D
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Q of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
Options:
A) 6x
B) 4x
C) 5x/3
D) 3x/2
E) 3x/5
Rationale: Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<Q<5x --> only option B fits.
Answer: B.
Answer: B
Question: There are 79 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?
Options:
A)2
B)4
C)8
D)49
E)32
Rationale: lets assign variables to all the areas in Venn Diagram of Three.
three different Units are DOG, Cat, Snake= Total = 79
Only Dog= d=15
Only Cat = c=10
Only Snake = s
Exactly Dog and Cat= 5
Exactly Dog and Snake = x
Exactly Cat and Snake = y
all three= 3
so 79=15+10+5+3+x+y+s
we need to know total snakes= x+y+s+3 = 49
answer:D
Answer: D
Question: A is 20% more efficient than B .how much time they will working together take to complete a job which A alone could have done in 15 days?
Options:
A)5 6/11 days
B)8 2/11 days
C)6 4/8 days
D)4 days
E)17 days
Rationale: The ratio of times taken by A and B=100:120=5:6
suppose B can do work in x days
then 5:6::15:x
x=6*15/5
x=18
A's 1 day's work=1/15
B's 1 day's work=1/18
(A+B)'s 1 day's work =1/15+1/18
A and B together can do work in 8 2/11 days
Answer(B)
Answer: B
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 60, what is the value of c âˆ’ a?
Options:
A)25
B)30
C)90
D)140
E)It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=120 --2
subtracting 1 from 2 we have
c-a=30;
ANSWER:B
Answer: B
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 190 different possible selections of the 2 members, how many members does the club have?
Options:
A)20
B)27
C)40
D)57
E)95
Rationale: Below is an answer to your question.
C2n=190Cn2=190 --> n!/2!∗(n−2)!=190. Now, notice that n!=(n−2)!∗(n−1)∗n so (n−2)!∗(n−1)∗n2!∗(n−2)!=190 --> (n−1)∗n/2=190 (n−1)n=380 --> n=20
Answer: A.
Answer: A
Question: In how many ways 3 boys and 3 girls can be seated in a row so that they are alternate.
Options:
A)144
B)288
C)36
D)256
E)None
Rationale: Solution: Let the Arrangement be,
B G B G B G B
34 boys can be seated in 3! Ways.
Girl can be seated in 3! Ways.
Required number of ways,
= 3!*3! = 36.
Answer: Option C
Answer: C
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 55km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
Options:
A)8.95km/hr
B)26.7km/hr
C)27.8km/hr
D)29.3km/hr
E)8.45km/hr
Rationale: average speed = (2*55*20)/55+20 km/hr
=29.3 km/hr
Answer (D)
Answer: D
Question: Which of the following expressions CANNOT have a negative value
Options:
A)|a + b| – |a – b|
B)|a + b| – |a|
C)a^2 + b^2
D)|2a + b| – |a + b|
E)|a^3 + b^3| – a – b
Rationale: Whenever you are required to find if the equation is a perfect square or not, try to bring everything in the form of a perfect square as they are always positive.
Of the given options, only option D can be written in from of a perfect square.
a^2+b^2
This will always be positive.
Correct Option: C
Answer: C
Question: (2^2-1)(2^2+1)(2^4+1)(2^10+1)=
Options:
A)2^18 - 1
B)2^16 + 1
C)2^32 - 1
D)2^128 - 1
E)2^16(2^16-1)
Rationale: A: is correct
(2^2-1)* (2^2+1)=(2^4-1)
(2^4-1)*(2^4+1)=2^8-1
(2^8-1)*(2^10 +1)=2^18-1
You can apply to this formula: a^2- b^2=(a-b)*(a+b)
Answer: A
Question: A committee of three people is to be chosen from 6 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)16
B)24
C)26
D)30
E)160
Rationale: One of the approaches:
Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 6 to send only onerepresentativesto the committee: 6C3=20.
But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.
Total # of ways: 6C3*2^3=160.
Answer: E.
Answer: E
Question: Ramesh can finish a piece of work in 12 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
Options:
A)8/3 days
B)4 days
C)5 days
D)11/3 days
E)7/3 days
Rationale: Ramesh can finish a piece of work in 12 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 6 days.
days needed to finish the same amount of work = 1/(1/6+1/12)=4 days
ANSWER:B
Answer: B
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/6%
B)16 8/3%
C)16 7/3%
D)16 2/3%
E)12 2/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer:D
Answer: D
Question: he population of a city is 130,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
Options:
A)146069
B)146067
C)156068
D)146068
E)179718
Rationale: Population after n years = P [1 + (R/100)]2
Population after 2 years = 130000 * [1 + 6/100]2 = (130000 x 53/50 x 53/50) = 146068
ANSWER: D
Answer: D
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/10
B)2/5
C)2/7
D)5/7
E)None
Rationale: Solution
P(getting a prize)	= 10 / (10+25)
‹=› 10 / 35
‹=› 2 / 7.
Answer C
Answer: C
Question: The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
Options:
A)11 years
B)77 years
C)88 years
D)10 years
E)66 years
Rationale: Let their ages be x and (x + 20) years.
5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years
Answer: D
Answer: D
Question: A profit of Rs. 600 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
Options:
A)s. 220
B)s. 120
C)s. 320
D)s. 50
E)s. 90
Rationale: A profit of Rs. 600 is divided between X and Y in the ratio of 1/2 : 1/3 or 3:2.
so profits are 360 and 240.
difference in profit share = 360-240=120
ANSWER:B
Answer: B
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 4 students is 14 years and that of the other 10 students is 16 years. The age of the 15th student is
Options:
A)9 years
B)11 years
C)14 years
D)21 years
E)9 years
Rationale: Solution
Age of the 15th student	=[15x15-(14x4+16x10)]
= (225 - 216)
= 9 years.
Answer E
Answer: E
Question: If x and y are positive real numbers such that x + y = 1, which of the following could be the value of 100x + 700y?
I. 90
II. 250
III. 699
Options:
A)II only
B)III only
C)I and II
D)I and III
E)II and III
Rationale: We know that x and y are both between 0 and 1.
The minimum limit of 100x + 700y is 100, when x is close to 1 and y is close to 0.
The maximum limit of 100x + 700y is 700, when x is close to 0 and y is close to 1.
The expression can take on any value between 100 and 700.
The answer is E.
Answer: E
Question: In the first 8 overs of a cricket game, the run rate was only 2.3 What should be the rate in the remaining 20 overs to reach the target of 260 runs?
Options:
A)12.08
B)12.18
C)12.0
D)6.19
E)6.21
Rationale: Required run rate
= [260- (2.3 * 8)]/20
= 241.60/20
= 12.08
Answer:A
Answer: A
Question: After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.2 cubic inches, what is the original volume of the cubic ice, in cubic inches?
Options:
A)2.5
B)3.2
C)4.0
D)6.5
E)8.0
Rationale: Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x
(1/16)x = 0.2
x = 3.2
Alternate solution: Try to backsolve.
Initial volume = 3.2
After one hour --> (1/4)3.2 = 0.8
After two hours --> (1/4)0.8 = 0.2
Answer: B
Answer: B
Question: 5, 25, 61, 113, ?
Options:
A)182
B)337
C)278
D)266
E)181
Rationale: ANSWER: A
Answer: A
Question: In a box, there are 10 red, 6 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither red nor blue?
Options:
A)4/51
B)10/21
C)7/12
D)6/21
E)13/17
Rationale: Total number of balls = 10+6+5 = 21
E = event that the ball drawn is neither red nor blue
= event that the ball drawn is blue
n(E) = 6
P(E) = 6/21
Answer is D
Answer: D
Question: A man has Rs. 192 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 ?
Options:
A)37
B)36
C)22
D)90
E)28
Rationale: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 192 16x = 192 x = 12.
Hence, total number of notes = 3x = 36.
Answer:B
Answer: B
Question: If a, b, q are integers, 33 = abq, and a < b < q, what is the smallest possible value of a?
Options:
A)-33
B)-3
C)1
D)3
E)11
Rationale: Given : a * b * q = 33.
33 is a Positive Odd number.Side Note:Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).
We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.
Correct answer is A
Answer: A
Question: Six points lie on the circumference of a ellipse. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
Options:
A)4
B)6
C)5
D)15
E)20
Rationale: Number of triangles can be formed out of 6 points= 6C3=20
Number of quadrilaterals can be formed out of 6 points= 6C4=15
20-15=5.
Answer=C
Answer: C
Question: What is the value of: 7^9 - 7^11 ?
Options:
A) -7^20
B) 7^-3
C) -49^20
D) -48(7^9)
E) 50(7^9)
Rationale: 7^9 - 7^11 = 7^9 (1 - 7^2) = 7^9 (1 - 49) = -48 (7^9), Answer D.
Answer: D
Question: Two letters from the word FARTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Two letters from the word FARTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Options:
A)A)1/500
B)B)1/28
C)C)27/28
D)D)124/125
E)E)499/500
Rationale: There are 6 consonants and 2 vowels in FARTHING.
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 ------> C.
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
A)150 m
B)155 m
C)180 m
D)190 m
E)205 m
Rationale: Answer: Option A
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (distance) = speed * Time
(50/3) * 9 = 150 meter
Answer: A