mathewhe/aqua_rat huggingface dataset:
Question: Two trains 140m and 160m long run at the speed of 60kmph and 40kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
(A) 5.6sec
(B) 8.9sec
(C) 10.8sec
(D) 12.6sec
(E) 15sec
Rationale: Relative speed = 60+40 = 100kmph * 5/18 = 250/9 m/s
Distance covered in crossing each other = 140+160 = 300m
Required time = 300*9/250 = 54/5 = 10.8sec
Answer is C
Answer: (C) 10.8sec
Question: You collect pens. Suppose you start out with 10. Mike gives you another 22 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 19 pens. How many pens do you have at the end?
(A) 39
(B) 40
(C) 41
(D) 42
(E) 59
Rationale: Solution
Start with 10 pens.
Mike gives you 22 pens: 10 + 22 = 39 pens.
Cindy doubles the number of pens you have: 39 Ã— 2 = 78 pens.
Sharon takes 19 pens from you: 78 - 19 = 59 pens.
So you have 59 at the end.
Correct answer: E
Answer: (E) 59
Question: If a and b are odd integers, which of the following is an even integer?
(A) a+ab+b
(B) a+ab+2b
(C) 4a+ab+2b
(D) 3a+ab+5b
(E) 3a+ab-b
Rationale: a+ab+2b=odd+odd+even=even
The answer is B.
Answer: (B) a+ab+2b
Question: When a merchant imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $101.50, what was the total value of the item?
(A) $1,850
(B) $2,450
(C) $2,750
(D) $3,150
(E) $3,450
Rationale: Let x be the value in excess of $1,000.
0.07x = 101.5
x = $1,450
The total value was $1,450 + $1,000 = $2,450.
The answer is B.
Answer: (B) $2,450
Question: The average (arithmetic mean) of 10, 20, and 60 is 5 more than the average of 10, 40, and what number?
(A) 25
(B) 60
(C) 50
(D) 30
(E) 40
Rationale: a1 = 90/3 = 30
a2 = a1 -5 = 25
sum of second list = 25*3 = 75
therefore the number = 75 -50 = 25
A
Answer: (A) 25
Question: Find the slope of the line perpendicular to the line y = (1/4)x - 7
(A) 1
(B) 2
(C) -4
(D) 4
(E) 5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 4. If m is the slope of the line perpendicular to the given line, then
m × (1/4) = -1
Solve for m
m = - 4
correct answer C) -4
Answer: (C) -4
Question: Car A is 30 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
(A) 1.5
(B) 4.5
(C) 4.75
(D) 3.75
(E) 3.5
Rationale: Relative speed of car A is 58-50=8 miles per hour, to catch up 30 miles and drive 8 miles ahead so to drive 38 miles it'll need 38/8=3.5 hours.
Answer: C
Answer: (C) 4.75
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
(A) 2
(B) 8
(C) 9
(D) 6
(E) 1
Rationale: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer:B
Answer: (B) 8
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is?
(A) 5230
(B) 5330
(C) 5331
(D) 5332
(E) 5336
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336
E)
Answer: (E) 5336
Question: Subtracting 10% from X is the same as multiplying X by what number?
(A) 12
(B) 90
(C) 26
(D) 27
(E) 18
Rationale: X - (10/100) X = X * ?
? = 90%
Answer:B
Answer: (B) 90
Question: If the Average (mean ) of 7 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 4x
(C) 5x/3
(D) 3x/2
(E) 3x/5
Rationale: Let the 5 numbers be 1,2,3,4,5,6,7 (since no restrictions are given). There mean is 4 (x).
Now the sum of greatest three would be 5+6+7= 18
so the answer has to be 6x....that is option A
Answer: (A) 6x
Question: If p and r are integers, and p^2 = 28r, then r must be divisible by which of the following?
(A) 2
(B) 4
(C) 5
(D) 7
(E) 14
Rationale: Solution: for p to be an int 28 r must be whole square of a number.
28r= 7*2*2*r
to make it whole square we need 7
so r can must be divisible by 7y where y is itself a whole square.
so Answer is D
Answer: (D) 7
Question: the efficiency of doing work of A is triple than B.hence,any work finished by A,60 days before than B.both together in how many days will finish the work?
(A) 20 days
(B) 45/2 days
(C) 25 days
(D) 30 days
(E) 28 days
Rationale: let any work finished by B in x days.A will take=(x-60) days
work of A in 1 days=3*(work of B in 1 days)
1/(x-60)=3*1/x,x=3(x-60),2x=180,x=90.
so,B take=90 days and A take=(90-60) days=30 days
(A+B) work in 1 days=(1/30+1/90)=4/90=2/45
so, together will finish work in 45/2 days
answer B
Answer: (B) 45/2 days
Question: If a fair die is rolled twice, what is the probability that a 2 occurs on at least one roll?
(A) 11/36
(B) 125/216
(C) 9/36
(D) 1/3
(E) 25/36
Rationale: Probability of no 2s is 5/6 * 5/6 = 25/36, so the probability of at least one 2 is 1 - (25/36) = 11/36
The correct answer is therefore A.
Answer: (A) 11/36
Question: Suppose you want to buy three loaves of bread that cost $1.75 each
and a jar of peanut butter that costs $3. A jar of jelly is $2.75, but you
donâ€™t need any jelly. You have $24. How much money will you have left
over?
(A) $15.75
(B) $12.50
(C) $13.50
(D) $14.50
(E) $51.50
Rationale: The jelly is extra information. 24.00 â€“ 3 x 1.75 â€“ 3.00 =
24.00 â€“ 5.25 â€“ 3.00 = 15.75.
You have $5.75 left.
correct answer A
Answer: (A) $15.75
Question: Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long it will take to fill the tank ?
(A) 10 mins
(B) 12 mins
(C) 15 mins
(D) 20 mins
(E) 25 mins
Rationale: Explanation:
In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as
Part filled by A in 1 min = 1/20
Part filled by B in 1 min = 1/30
Part filled by (A+B) in 1 min = 1/20 + 1/30
= 1/12
So both pipes can fill the tank in 12 mins.
Option B
Answer: (B) 12 mins
Question: N = 1/2 + 5/7
Find N
(A) 13/14
(B) 16/18
(C) 3/4
(D) 17/14
(E) 1/2
Rationale: N = 1/2 + 5/7
Multiply both the denominators 2 * 7 = 14
Multply 14 by both sides
14 * N = 14 * 1/2 + 14 * 5/7
14 * N = 7 + 10
14 * N = 17
N = 17/14
Ans: D
Answer: (D) 17/14
Question: How many digits will be there to the right of the decimal point in the product of 95 and .02554 ?
(A) 6
(B) 7
(C) 4
(D) 5
(E) 8
Rationale: product of 95 and .02554 is 2.4263.
Therefore number of digits to right of decimal point is 4
Answer is C.
Answer: (C) 4
Question: If 45% of a class averages 100% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 65% on the test, what is the overall class average? (Round final answer to the nearest percent).
(A) 86%
(B) 87%
(C) 88%
(D) 89%
(E) 90%
Rationale: This question is a Weighted Average question with a series of dependent variables.
The remaining portion of the class represents 100% - 45% - 50% = 5% of the class
Converting the portions of the class population to decimal weights, we find:
Class Average = 0.45x100 + 0.50x78 + 0.05x63 = 87.15
The class average (rounded) is 87%
Final Answer
B) 87%
Answer: (B) 87%
Question: 3 ltr of water is added with 9 ltr of a solution containing 57%of alcohol in the water. The % of alcohol in the new mixture is?
(A) 41.5%
(B) 42.75%
(C) 43%
(D) 45%
(E) 45.75%
Rationale: We have a 9 litre solution containing 57% of alcohol in the water.
=> Quantity of alcohol in the solution
=9Ã—57/ 100
Now 3 litre of water is added to the solution.
=> Total quantity of the new solution = 9 + 3 = 12
Percentage of alcohol in the new solution
=9Ã—57/100
12
Ã—
100
=9Ã—5710012Ã—100
=9Ã—4.75/100
=42.75%
B
Answer: (B) 42.75%
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.48 per glass on the first day, what was the price per glass on the second day?
(A)  $015
(B)  $0.20
(C)  $0.30
(D)  $0.32
(E)  $0.45
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.48=3*x --> x=$0.32.
Answer: D.
Answer: (D)  $0.32
Question: Set Q consists of the following five numbers: Q = {5, 7, 13, 21, 34}. Which of the following sets has the same standard deviation as Set Q?
I. {35, 38, 43, 51, 64}
II. {10, 16, 26, 42, 68}
III. {46, 59, 67, 72, 75}
(A)  I only
(B)  III
(C)  IIII
(D)  IIIII
(E)  I, II,III
Rationale: (1)	Multiplying all the numbers change Standard Deviation
(2)	Adding and subtracting all the numbers with the same number keeps the standard deviation same.
If you observe Set I and III are added versions of Set Q .
Set I: 5 has been added to the Set Q
Set III: Subtract each element from 80 and you would find a number there in the Set Q.
Set II: elements are multiplied by 2 and standard deviation changes.
Hence the answer is B.
Answer: (B)  III
Question: A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
(A) 2
(B) 6
(C) 7
(D) 9
(E) 8
Rationale: Explanation:
Quantity of milk in the mixture = 90/100 (70) = 63 litres.
After adding water, milk would form 87 1/2% of the mixture.
Hence, if quantity of mixture after adding x liters of water, (87 1/2) / 100 x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
Answer: A
Answer: (A) 2
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 28 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
(A) 16
(B) 24
(C) 32
(D) 40
(E) 48
Rationale: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.28(800) = 216
The answer is A.
Answer: (A) 16
Question: In a certain sequence, the first term is 6, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence?
(A) 13/8
(B) 21/13
(C) 8/5
(D) 33/20
(E) 8/13
Rationale: let five terms in the sequence be a,b,c,d,e
a=6
b= 1+1/6=7/6
c=1+6/7= 13/7
d= 1+7/13 = 20/13
e= 1+13/20 = 33/20
hence answer should be D.
Answer: (D) 33/20
Question: What is the unit digit in 7^100?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: Unit digit in 7^100 = unit digit in [(7^4)^25 ]
But unit digit in 7^4=1
unit digit 7^100= 1
Answer is B
Answer: (B) 1
Question: How many consonants are present between the first and fifth vowel in the sequence of English alphabet ?
(A) 12
(B) 13
(C) 11
(D) 16
(E) None of these
Rationale: Explanation:
Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The first and fifth vowels are A and U respectively. There are 19 letters between A and U; out of which 'E' , 'I' and 'O' are vowels. Thus, there are 16 consonants between A and U.
ANSWER D
Answer: (D) 16
Question: After decreasing 24% in the price of an article costs Rs.760. Find the actual cost of an article?
(A) 1218
(B) 2777
(C) 1000
(D) 2688
(E) 1991
Rationale: CP* (76/100) = 760
CP= 10 * 100 => CP = 1000
Answer: C
Answer: (C) 1000
Question: A survey was sent to 60 customers, 7 of whom responded. Then the survey was redesigned and sent to another 72 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
(A) 2%
(B) 7%
(C) 14%
(D) 28%
(E) 63%
Rationale: Rate of first survey = 7/60
Rate of second survey = 9/72
% Response rate increase (9/72-7/60)/(7/60) = 7%
Answer is B = 7%
Answer: (B) 7%
Question: A dozen bananas and 5 pounds of apples are currently at the same price. If the price of a dozen bananas rises by 5 percent and the price of apples rises by 5 %. How much more will it cost to buy a dozen bananas and 5 pounds of apples .
(A) 5%
(B) 15%
(C) 25%
(D) 14%
(E) 10%
Rationale: Say currently both a dozen bananas and 5 pounds of apples cost $100 (they are at the same price). So, to buy a dozen bananas and 5 pounds of apples we need $200.
After the increase, the price of a dozen bananas will be $105 and the price of 5 pounds of apples will be $105. So after the increase, to buy a dozen bananas and 5 pounds of apples we'll need $210.
Increase = 10%.
Answer: E.
Answer: (E) 10%
Question: If the product of 3 consecutive integers is 210 then the sum of the two smaller integers is:
(A) 17
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: let the numbers be x-1 , x , x+1
(x-1)(x)(x+1)=210
210=2*105
=2*3*35
=2*3*5*7
this can be written as 6*5*7
=>x-1=5
x=6
x+1=7
sum of two smallest numbers=6+5=11
ANSWER:C
Answer: (C) 11
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 482
(B) 887
(C) 299
(D) 277
(E) 200
Rationale: 20000(11/10)4 - 20000(6/5)2 = 482
Answer: A
Answer: (A) 482
Question: 8 : 18 : : 24 : ?
(A) 38
(B) 32
(C) 44
(D) 43
(E) 42
Rationale: 3^2-1=8
4^2+2=18
5^2-1=24
there for
6^2+2=38
ANSWER:A
Answer: (A) 38
Question: Rajesh can finish 1/4 of his home work in one hour. Seema can finish 3/7 of
her homework in 30 minutes and Ramya can finish 3/4 of her homework in
two and a half hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.30 PM for 30 minutes?
(A) 4:30pm
(B) 5:30pm
(C) 6:30pm
(D) 5:10pm
(E) 3:30pm
Rationale: ajesh can finish his work in 4 hr,
ramya can finish her work in 1 hr
seema can finish in 3.3 hr
so 4:30pm they can go to play
ANSWER:A
Answer: (A) 4:30pm
Question: Nine animals of a circus has to be placed inside in nine cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
(A) A.6048
(B) B.10825
(C) C.14400
(D) D.784200
(E) E.302400
Rationale: ways for cages that are too small = 5*4*3*2=120
since we have 5 cages and 5 animal left therefore ways for 5 cages =5!
total ways =120*5!=14400
Answer C
Answer: (C) C.14400
Question: Find the average of first 20 natural numbers.
(A) 20.5
(B) 18
(C) 19.5
(D) 10.5
(E) 17
Rationale: Exp. Sum of first n natural numbers = n( n+1)/2
So, sum of first 20 natural numbers = 20*21/2 = 210
Required average =210/20 =10.5
Answer:D
Answer: (D) 10.5
Question: Akash leaves Chennai at 6am & reaches Bangalore at 10am. Prakash leaves Hyderabad at 8am and reaches Chennai at 11:30am. At what time do they cross each other?
(A) 6 : 32am
(B) 7 : 56am
(C) 8 : 56am
(D) 3 : 56am
(E) 5 : 56am
Rationale: Time taken by Akash = 4 h
Time taken by Prakash = 3.5 h
For your convenience take the product of times taken by both as a distance.
Then the distance = 14km
Since, Akash covers half of the distance in 2 hours(i.e at 8 am)
Now, the rest half (i.e 7 km) will be coverd by both prakash and akash
Time taken by them = 7/7.5 = 56 min
Thus , they will cross each other at 8 : 56am.
C
Answer: (C) 8 : 56am
Question: A certain auto manufacturer sold 5% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.2 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
(A) 17,00,000
(B) 18,00,000
(C) 19,00,000
(D) 21,00,000
(E) 21,90,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-5/100(X)
If sales in 2006,X= 2.2 million find X-5/100(X)
(2.2 x 10^6)-5/100(2.2 x 10^6)
2200000-1,10,000=20,90,000-----> 21,00,000(approx)
Answer-D
Answer: (D) 21,00,000
Question: A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability T that both selected dogs are NOT littermates?
(A) 1/6
(B) 2/9
(C) 5/6
(D) 7/9
(E) 8/9
Rationale: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.
So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.
Work with probabilities:
Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).
The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).
The probability of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).
The required probability is 1/2 + 1/3 = 5/6.
Find the probability for the complementary event: choose AA or BB.
Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.
Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 = 1/12.
Again, we obtain 1 - (1/12 + 1/12) T= 5/6.
Answer: C
Answer: (C) 5/6
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
(A) 2%
(B) 8%
(C) 5%
(D) 6%
(E) 1%
Rationale: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B
Answer: (B) 8%
Question: What is the lowest positive integer that is divisible by each of the odd integers between 11 and 17, inclusive?
(A) 3*5*13*17*11
(B) 5×17×19×23
(C) 7×15×17×19
(D) 7×15×19×21
(E) 3*4*13*17*11
Rationale: We should find the LCM of 11,13,15 = 3*5, 17,-> LCM = 3*5*13*17*11 .
Answer: A.
Answer: (A) 3*5*13*17*11
Question: In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be?
(A) 100 cu.m
(B) 1000 cu.m
(C) 10000 cu.m
(D) 2000 cu.m
(E) 4000 cu.m
Rationale: 20 * 10 * 5 = 1000
ANSWER:B
Answer: (B) 1000 cu.m
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 9
(C) 6
(D) 5
(E) 2
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer:A
Answer: (A) 8
Question: A bag of potatoes weighs 60 lbs divided by half of its weight. How much does the bag of potatoes weight?
(A) 20 lb
(B) 11 lb
(C) 10 lb
(D) 15 lb
(E) 5 lb
Rationale: Sol.
66÷6 = 11.
Answer : B
Answer: (B) 11 lb
Question: Let F(m,n) =45*m+36*n,where m and n are integers (+ve or -ve) What is the minimum positive value for f(m,n) (This may be achived for various values of m and n)?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: f(m,n)=45*m+36*n
putting m=1,n=-1 in above eqn we get
f(m,n)=45*1+36*(-1)
=9.
ANSWER:E
Answer: (E) 9
Question: The bankerâ€™s discount on Rs. 1600 at 10% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
(A) 2 months
(B) 4 months
(C) 6 months
(D) 7 months
(E) None
Rationale: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 10%.
âˆ´ Time = [100 * 80 / 1600 * 10] year = 1/2 year = 6 months.
Answer C
Answer: (C) 6 months
Question: A and B are two numbers. Let
@(A,B)= Average of A and B,
/(A,B)= Product of A and B, and
*(A,B)= The result of dividing A by B.
The sum of A and B is given by
(A) /(@(A,B),2)
(B) @(*(A,B),2)
(C) @(/(A,B),2)
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Assume some values for A and B and substitute in the options to get the answer.
Here, Let A = 1 and B = 2.
So, /(@(A,B),2) = /(@(1,2),2)
= /(1.5,2) = 3
= Sum of A and B.
Answer : A
Answer: (A) /(@(A,B),2)
Question: An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 520 km/hr
(B) 640 km/hr
(C) 656 km/hr
(D) 731 km/hr
(E) 720 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x	3	km/hr	= 720 km/hr.
5
E
Answer: (E) 720 km/hr
Question: If K is a negative integer, which of the following must be a negative integer?
(A) K + 1
(B) K/2+3
(C) K^4
(D) K – y
(E) K^11
Rationale: We need to check each option here:
A.K + 1
This will depend on the value of K. Nothing can be said
B. K/2+3
This will depend on the value of K. Nothing can be said
C. K^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. K – y
This will depend on the value of K. Nothing can be said
E. K^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative
Correct Option: E
Answer: (E) K^11
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 7 ½ hours if they are walking in the same direction?
(A) 7 km
(B) 6 km
(C) 9 3/8 km
(D) 9 km
(E) 5 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 7 ½ h.
D = 5/4 * 15/2 = 75/8
= 9 3/8 km
Answer:C
Answer: (C) 9 3/8 km
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
(A) 2/23
(B) 3/25
(C) 9/42
(D) 1/21
(E) 2/25
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: (C) 9/42
Question: If a jogger jogs 16 km/hr instead of 12 km/hr, he would have jogged 10 km more. The actual distance he jogged is
(A) 50 km
(B) 40 km
(C) 30 km
(D) 20 km
(E) None of these
Rationale: Explanation :
The actual distance jogged be d.
=> d/12 = (d+10)/16
=> 16d = 12d+120
=> 4d = 120
=> d = 30
Answer : C
Answer: (C) 30 km
Question: A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?
(A) 7 cm
(B) 2 cm
(C) 8 cm
(D) 3 cm
(E) 9 cm
Rationale: Volume of the wire (in Cylindrical shape) is equal to the volume of the sphere.
π(16)2 * h = (4/3)π (12)3 => h
= 9 cm
Answer:E
Answer: (E) 9 cm
Question: In what time will two trains cross each other completely, which are running on the same parallel lines in opposite directions, each train running with a speed of 60 kmph being 130 m and 120 m in length respectively?
(A) 6.9 sec
(B) 7.1 sec
(C) 7.2 sec
(D) 7.4 sec
(E) 7.5 sec
Rationale: D = 130m + 120m = 250m * 1/1000 = 0.25 kms
RS = 60 + 60 = 120 kmph
T = (0.25/120) * 3600 = 7.5 sec
ANSWER:E
Answer: (E) 7.5 sec