mathewhe/aqua_rat huggingface dataset:
Question: If x is the sum of a consecutive positive integers. y is the sum of b consecutive positive integers. For which of the following values of a and b is it impossible that x = y?
(A) a = 2; b = 6
(B) a = 3; b = 6
(C) a = 7; b = 9
(D) a = 10; b = 4
(E) a = 10; b = 7
Rationale: I approached this in a different way, although may be longer but it's certainly more intuitive
It is impossible that x = y if one of them is necessarily even while the other is necessarily odd
for two consecutive integers the sum is necessarily odd
for six consecutive integers the sum is necessarily odd (sum of 3two consecutive integerswhich are all odd)
Thus A is incorrect.
The sum of 3 consecutive integers can be even or odd (an odd integer from the first 2 + an additional integer which can be even or odd). Thus B is incorrect. You can do a similar approach for C and E (it follows that the sum of a specified odd number of consecutive integers can be odd or even).
Leaving us with D to be the only not-wrong answer. To confirm, you can easily deduce that the sum of 4 consecutive integers (sum of 2 odd integers) is necessarily even while the sum of 10 consecutive integers (sum of 5 odd integers) is necessarily odd. Thus D is the right answer.
Answer: (D) a = 10; b = 4
Question: How many four letter words are formed using the letters of the word PRESS?
(A) A)30
(B) B)60
(C) C)90
(D) D)120
(E) E)150
Rationale: The number of letters in the given word is five.
The number of three letter words that can be formed using these four letters is 5P4
= 5 *4 * 3*2 = 120.
Answer:D
Answer: (D) D)120
Question: If a<0, which of the following represents a positive number?
(A) a/ |a|
(B) -a|a|
(C) a|a|
(D) |a|/a
(E) |a|a
Rationale: Answer : B
Answer: (B) -a|a|
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 10 years at the same rate?
(A) 10 years
(B) 11 years
(C) 77 years
(D) 88 years
(E) 55 years
Rationale: P ---- 2P ---- 8 years
2 1/4 P ---- 10 years
Answer:A
Answer: (A) 10 years
Question: ABCD is a square. F and E are the midpoints of sides AD and CD, respectively. The area of triangle FED is 2 square inches. What is the area of square ABCD (in square inches)?
(A) 4
(B) 8
(C) 16
(D) 32
(E) 64
Rationale: Area of FED = 2 sq inches = 1/2*DE*FD = 1/2*DE^2
Because the sides of a square are equal, hence half of the sides will also be equal.
DE^2 = 4
DE = FD = 2
Hence the side of the square = 4
Area if the square = 4*4 = 16
Correct Option: C
Answer: (C) 16
Question: What is the difference between the largest number and the least number written with the digits 9, 2, 1, 5?
(A) 6084
(B) 3788
(C) 2077
(D) 8262
(E) 1812
Rationale: Explanation:
1259
9521
------------
8262
Answer:D
Answer: (D) 8262
Question: A tradesman by means of his false balance defrauds to the extent of 25%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 17%
(B) 77%
(C) 44%
(D) 56.25%
(E) 47%
Rationale: g% = 25 + 25 + (25*25)/100
= 56.25%
Answer: D
Answer: (D) 56.25%
Question: 33 1/3% of 36?
(A) 16
(B) 21
(C) 18
(D) 12
(E) 18
Rationale: Explanation:
33 1/3 % = 1/3
1/3 * 36 = 12
Answer: Option D
Answer: (D) 12
Question: The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 256,000 locusts?
(A) 12
(B) 14
(C) 16
(D) 15
(E) 11
Rationale: - 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
+ 8 hours: 64,000
+ 10 hours: 128,000
+ 12 hours: 256,000
Answer : A
Answer: (A) 12
Question: If the price of a TV is first decreased by 20% and then increased by 30%, then the net change in the price will be :
(A) 4% increase
(B) 10% increase
(C) 10% decrease
(D) 6% increase
(E) None of these
Rationale: Explanation :
Solution: let the original price be Rs. 100.
New final price = 130% of(80% of 100) =Rs. 130/100 * 80/100 * 100 = Rs. 104.
.'. Increase = 4%
Answer : A
Answer: (A) 4% increase
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Explanation:
2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,
Then 30 ~ 40 = 10
===> 1 -----> 10
===> 2 -----> 20
Answer: Option B
Answer: (B) 20
Question: 286, 462, 362, 527, 671, 253
(A) 286
(B) 462
(C) 352
(D) 537
(E) 671
Rationale: In each number except 537, the middle digit is the sum of other two.
Answer: Option D
Answer: (D) 537
Question: In a family 15 people eat only vegetarian, 8 people eat only non veg., 11 people eat both veg and non veg.. How many people eat veg in the family?
(A) 20
(B) 11
(C) 23
(D) 26
(E) 21
Rationale: Total people eat veg = only veg + both veg and non veg
Total= 15+11= 26
Answer = D
Answer: (D) 26
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 375
Rationale: Explanation:
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
ANSWER IS C
Answer: (C) 322
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $130, how much more remains to be paid?
(A) $880
(B) $990
(C) $1,000
(D) $1,170
(E) $1,210
Rationale: 10/100P = 130 >> p= 130*100/10 = 1300
1300 - 130 = 1170
ANSWER:D
Answer: (D) $1,170
Question: College T has 1000 students. Of the 180 students majoring in one or more of the sciences,120 are majoring in Chemistry and 120 are majoring in Biology. If at least 20 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
(A) 50 to 120
(B) 60 to 130
(C) 50 to 100
(D) 70 to 110
(E) 60 to 120
Rationale: Total = Chemistry + Biology - Both + Neither
180= 120 + 120 - Both + N
We know that N (Neither) must be at least 20, so set N=20 and solve:
180 = 120 + 120 - Both + 20
200 = 260 - Both
Both = 60
Even if you're not sure whether 60 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range,
Both can not be greater than 120, because even if every chemistry major was also a biology major, there are only 120 chemistry majors total. E the solution.
Answer: (E) 60 to 120
Question: A sells a bicycle to B and makes a profit of 20%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A.
(A) 237
(B) 126
(C) 971
(D) 611
(E) 150
Rationale: Explanation:
ANSWER: E
Answer: (E) 150
Question: What is the value of x^2yz − xyz^2, if x = − 2, y = 1, and z = 1?
(A)  6
(B)  24
(C)  30
(D)  32
(E)  48
Rationale: 4*1*1 -(- 2*1*1)
=4+2 = 6
Ans: A
Answer: (A)  6
Question: What is the smallest positive integer which when increased by 1 is divisible by 22, 36, 26 and 21?
(A)  7271
(B)  36035
(C)  122149
(D)  22362621
(E)  4109
Rationale: 22 = 2*11
36 = 2 * 2 * 3 * 3
26 = 2 * 13
21 = 3 * 7
So the answer is (2 * 2 * 3 * 3 * 7 * 11 * 13) - 1 = 36035, which is option B.
Answer: (B)  36035
Question: A wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. What is the area of the wall photo, in square inches?
(A) 96
(B) 86
(C) 108
(D) 144
(E) 118
Rationale: This question is an example of a 'punch out' question - we have to find the area of EVERYTHING, then 'punch out' the part that we don't want.
We're told that a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches. We're asked for the area of the wall photo, in square inches.
Area of a rectangle = (length)(width)
So the area of the wall photo is... (8)(12) = 96
The wall photo 'adds' 2 inches to the top, bottom, left and right 'sides' of the picture, so the area of EVERYTHING is...
(8+2+2)(12+2+2) = (12)(16) = 196
When we 'punch out' the area of the paper, we'll be left with the area of the wall photo:
192 - 96 = 96
Final Answer:
A
Answer: (A) 96
Question: What was the day of the week on 17th June, 1998?
(A) Sunday
(B) Tuesday
(C) Friday
(D) Wednesday
(E) Suturday
Rationale: Explanation:
17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March April May June
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday
Answer: D) Wednesday
Answer: (D) Wednesday
Question: In a class of 25 students, 3 students did not borrow any books from the library, 11 students each borrowed 1 book, 6 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The total number of books the students borrowed is 25*2=50.
The students who borrowed zero, one, or two books borrowed 11*1+6*2=23 books.
The 5 students who borrowed at least three books borrowed 50-23=27 books.
If 4 of these students borrowed exactly 3 books, then the maximum that one student could have borrowed is 27-12= 15 books.
The answer is D.
Answer: (D) 15
Question: Two trains 180m and 360m long run at the speed of 60kmph and 30kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
(A) 21.6sec
(B) 8.9sec
(C) 10.8sec
(D) 12.6sec
(E) 15sec
Rationale: Relative speed = 60+30 = 90kmph * 5/18 = 25 m/s
Distance covered in crossing each other = 180+360 = 540m
Required time = 540*1/25 = 21.6 sec
Answer is A
Answer: (A) 21.6sec
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
(A) 2888
(B) 2669
(C) 3600
(D) 1279
(E) 1271
Rationale: P = 144(100/5)2 => P = 3600.Answer:C
Answer: (C) 3600
Question: Calculate the largest 4 digit number which is exactly divisible by 98?
(A) 9800
(B) 9898
(C) 9702
(D) 9604
(E) 9996
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 98 we get remainder 3
Hence largest 4 digit number exactly divisible by 98 = 9999 - 3 = 9996
E
Answer: (E) 9996
Question: When positive integer g is divided by 6, the remainder is 1. Which of the following must be true?
I. g is a prime number
II. g is odd
III. g is divisible by 7
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Rationale: g=6q+1
Examine II) put q=0,1,2,3....... we have g=1,7,13,...25 so g must be odd
Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true
Examine I) g= 7 true but while 2 is prime, it does not give reminder 1
Answer: B
Answer: (B) II only
Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 245
(B) 777
(C) 282
(D) 266
(E) 225
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30 = 25/2 => 2(150 + x) = 750 => x = 225 m.
Answer: E
Answer: (E) 225
Question: How many pieces of 75 cm can be cut from a rope 57 meters long?
(A) 30
(B) 40
(C) 76
(D) None
(E) Cannot be determined
Rationale: Explanation :
Total pieces of 75 cm that can be cut from a rope of 57 meters long is
= (57 meters)/(75 cm)
= (57 meters)/(0.75 meters)
= 76
Answer : C
Answer: (C) 76
Question: Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.7%, what fraction of the products was checked by worker y?
(A) 2/3
(B) 5/6
(C) 7/8
(D) 4/5
(E) 5/8
Rationale: x: 0.5% is 0.2%-points from 0.7%.
y: 0.8% is 0.1%-points from 0.7%.
Therefore the ratio of products checked by y:x is 2:1.
Thus, worker y checked 2/3 of the products.
The answer is A.
Answer: (A) 2/3
Question: The salary of Charan was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
(A) 12%
(B) 11.11%
(C) 11.5%
(D) 13%
(E) None of these
Rationale: Explanation :
Solution: Let the original salary be Rs. 100. new salary = Rs. 90.
Increase on 90 = 10
Increase on 100 = ?
= 10*100/90 = 11 1/9%.
Answer : B
Answer: (B) 11.11%
Question: A certain college party is attended by both male and female students. The ratio of male to female students is 4 to 5. If 15 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: The ratio is 4:5 = 8:10, so there are 8k males and 10k females.
If 15 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.
8k-5k = 15
k = 5
8k + 10k = 40 + 50 = 90
The answer is D.
Answer: (D) 90
Question: The length of a cold storage is double its breadth. Its height is 3 metres. The area of its four walls(including doors) is 108 m2. Find its volume.
(A) 206
(B) 216
(C) 226
(D) 246
(E) 288
Rationale: let xbe breadth ,then 2x is the length
then 2x*3*2+x*3*2=108
12x+6x=108
x=108/18=6
length 12,breadth 6 ,height 3
volume=12*6*3=216m^3
ANSWER:B
Answer: (B) 216
Question: A can contain a mixture of two liquids A and B in the ratio 7:5 when 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?
(A) 28 litres
(B) 21 litres
(C) 45 litres
(D) 36 litres
(E) None of these
Rationale: Explanation :
Let, the can initially contains 7x and 5x litres of mixtures A and B respectively.
When 9 litres of mixture are drawn off, quantity of A in mixture left :-
=>7x−(7/12)×9=7x−(21/4) litres.
Similarly, quantity of B in mixture left:
=>5x−(5/12)×9=5x−(15/4) litres.
The ratio becomes :
=>(7x−21)/(5x−(15/4)+9)=7/9.
=>(28x−21)/(20x+21)=7/9.
=>252x−189=140x+147.
=>112x=336.
=>x=3.
Hence, the required initial amount of A is :
=>7×x=7×3=21 litres.
Answer : B
Answer: (B) 21 litres
Question: A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 37
(B) 30
(C) 25
(D) 28
(E) 40
Rationale: Original no be a
let divisor be d & let the quotient of the division of a by d be x
=> a/d = x and the remainder is 24
a = dx+24
when twice the original no is divided by d, 2a is divided by d
=>the problem state that (2dx + 48) / d leaves a remainder of 11
2dx is perfectly divisible by d and will not leave remainder
the remainder of 11 was obtained by dividing 48 by d
when 48 is divided by 37 the remainder that one will obtain is 11
the divisor is 37
ANSWER A
Answer: (A) 37
Question: Two persons , Ram & Lakshman , who are at a distance of 100 km from each other, move towards each other from two places P and Q at speeds of 20 kmph and 25 kmph respectively. Lakshman reaches P, returns immediately and meets Ram at R, who started on the return journey to P immediately after reaching Q. What is the distance between Q and R?
(A) 33 1/3 km
(B) 25 km
(C) 30km
(D) 27 1/3 km
(E) 28 1/3 km
Rationale: Ram takes 100/20 = 5 hours to cover the distance from P to Q. By that time Lakshman covers
covers 5 *25 = 125 km
Lakshman covers 25 km more than the distance PQ . Now the distance between them = 75 km
Time taken by them to meet = Distance/ Relative speed = 75/(20+25) = 75/45 = 5/3 hrs.
Distance between Q and R is nothing but the distance covered by Ram in 5/3 hours = 20 *5/3 = 100/3 km or 33 1/3 km
ANSWER:A
Answer: (A) 33 1/3 km
Question: If f(x) = (x^2 - 1)/(x), what is f(1/x) in terms of f(x)?
(A) -1*f(x)
(B) f(x)
(C) 1/f(x)
(D) -1/f(x)
(E) 2*f(x)
Rationale: f(1/x) = ((1/x)2 - 1) / ((1/x))
= ((1/x^2) - 1) / (1/x)
= ((1-x^2)/(x^2)) / (1/x
= (1-x^2)/(x^2)
= - ( (x^4) -1) / (x)
= -1* f(x)
Answer is A.
Answer: (A) -1*f(x)
Question: Two watches are set for an alarm at 10 0'clock in the night. One watch gains 2 minutes per hour. When the faster watch shows 4:12 in the morning when the alarm rings what does the correct watch show?
(A) 5:00
(B) 4:00
(C) 4:10
(D) 5:20
(E) 6:00
Rationale: The faster watch gains 2 minutes per hour
The two watches show 10:00 at 10 0'clock
At 11 0'clock -
The correct watch is at 11:00
The faster watch is at 11:02 (1 hour + gains 2 minutes per hour)
At 12 midnight -
The correct watch is at 12:00
The faster watch is at 12:04 ( 2 hours + gains 4 minutes per 2 hours)
In 6 hours the faster watch gains 6*2 = 12 minutes and is at 4:12 and the correct watch is at 4:00
Answer is B
Answer: (B) 4:00
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :
(A) 45 kg
(B) 46 kg
(C) 47 kg
(D) 48 kg
(E) 49 kg
Rationale: Explanation:
Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg. Answer: A
Answer: (A) 45 kg
Question: which of the following inequalities indicates the set of all values of d for which the lengths A of the three sides of a triangle can be 3,4, and d?
(A) 0<d<1
(B) 0<d<5
(C) 0<d<7
(D) 1<d<5
(E) 1<d<7
Rationale: This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .
Thus,
|a-b| < c < a+b
|b-c| < a < b+c
|c-a| < b < a+c
Thus, if the sides of the triangle are 3,4 and d,
4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer.
Answer: (E) 1<d<7
Question: A train 125 m long passes a man, running at 9 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 35 km/hr
(B) 50 km/hr
(C) 54 km/hr
(D) 65 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 9) km/hr. x - 9 = 45 ==> x = 54 km/hr.
Answer: C
Answer: (C) 54 km/hr
Question: Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and time, If both are numerically equal.
(A) 1
(B) 8
(C) 5
(D) 4
(E) 2
Rationale: Explanation:
Let sum = X. Then S.I = 16x/25
Let rate = R% and Time = R years.
Therefore, (x * R * R)/100 = 16x/25 or R^2 = 1600/25, R = 40/5 = 8
Therefore, Rate = 8% and Time = 8 years.Answer:
B) Rate = 8% and Time = 8 years.
Answer: (B) 8
Question: if a die has 1 6 and 3 4 and 2 5 opposite each other how many such dies can be made
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: if one face have 1,3,2, then the corossponding face will be occupied by respective pair i.e (6,4,5).
so there r 3 place and we have 3 place soit can be arranged in 3! way i.e 6 way and every pair will be suffled in 2 way so ans will be6*2=12.
ANSWER:C
Answer: (C) 12
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train ?
(A) 27 7/9
(B) 28 7/9
(C) 29 7/9
(D) 30 7/9
(E) None of these
Rationale: Explanation:
As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec
Length of Train= Speed * Time
Length=50/9∗5
=250/9
=27 7/9
Option A
Answer: (A) 27 7/9
Question: If log1087.5 = 6.9421, then the number of digits in (875)10 is?
(A) 30
(B) 28
(C) 80
(D) 26
(E) 25
Rationale: X = (875)10 = (87.5 x 10)10
Therefore, log10X = 10(log1087.5 + 1)
= 10(6.9421 + 1)
= 10(7.9421) = 79.421
X = antilog(79.421)
Therefore, number of digits in X = 80.
ANSWER:C
Answer: (C) 80
Question: Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 670 then loss of Pyarelal?
(A) 603
(B) 703
(C) 800
(D) 903
(E) 1000
Rationale: Let the capital of Pyarelal be x, then capital of Ashok=x/9
So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x
Hence out of the total loss of 670, loss of Pyarelal= 670*9x/10x=603
ANSWER:A
Answer: (A) 603
Question: What is the sum of all remainders obtained when the first 120 natural numbers are divided by 9?
(A) 397
(B) 401
(C) 403
(D) 405
(E) 399
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=405.
Answer: D.
Answer: (D) 405
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
(A) 11 1/2 days
(B) 15 1/2 days
(C) 15 1/2 days
(D) 16 1/2 days
(E) 12 1/2 days
Rationale: E
12 1/2 days
15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer: (E) 12 1/2 days
Question: What should be added to 4440 so that it may become a perfect square?
(A) 44
(B) 45
(C) 46
(D) 47
(E) 49
Rationale: 67x67=4489
4489-4440 = 49
If added to 49 get perfect square
answer =E
Answer: (E) 49
Question: The average weight of a group of boys is 20 kg. After a boy of weight 33 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 12
(B) 14
(C) 18
(D) 24
(E) 10
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 33 kg joins the group, total weight of boys = 20x + 33
So 20x + 33 = 21(x + 1) = > x = 12.
ANSWER:A
Answer: (A) 12
Question: The sides of a rectangular field are in the ratio 3 : 4. If the area of the field is 9408 sq. m, the cost of fencing the field @ 25 paise per metre is
(A) Rs. 55.50
(B) Rs. 67.50
(C) Rs. 86.50
(D) Rs. 98.00
(E) None of these
Rationale: Solution
Let length = (3x) metres and breadth = (4x) metres.
Then, 3x × 4x = 9408 ⇔ 12x2 = 9408 ⇔ x2 = 784 ⇔ x = 28.
So, length = 84 m and breadth = 112 m.
Perimeter = [2(84 + 112)] m = 392 m.
∴ Cost of fencing = Rs. (0.25 × 392) = Rs. 98.00. Answer D
Answer: (D) Rs. 98.00
Question: A 600 meter long train crosses a signal post in 20 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 2 min
(C) 8 min
(D) 9 min
(E) 5 min
Rationale: S = 600/20 = 1530 mps
S = 3600/30 = 120 sec = 2 min
Answer: B
Answer: (B) 2 min
Question: If the speed of a man is 66 km per hour, then what is the distance traveled by him in 30 seconds ?
(A) 550m
(B) 500m
(C) 375 m
(D) 420 m
(E) 440 m
Rationale: The distance traveled in 30 sec = 66*(5/18) *30 =550m
ANSWER:A
Answer: (A) 550m
Question: In a family gathering, there is a basket in which there are oranges, bananas and apples. Half of the people in the family eat oranges, half of the other half eat bananas and the rest eat apples. If the number of people who eat oranges are 10 less than the total number of people, find the number of people in the gathering.
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Let the number of people who eat oranges be X. Then,
total number of people= X + (X/2) + (X/2)= 2X
=> 2X-10=X
=>X=10
=> Total number of people were 2X=20
Option D
Answer: (D) 20