mathewhe/aqua_rat huggingface dataset:
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 3.6
(B) 7.2
(C) 8.4
(D) 10
(E) 9
Rationale: Speed=(600/5 * 60) m/sec
= 2 m/sec.
Converting m/sec to km/hr
=(2*18/5) km/hr
= 7.2 km/hr.
Answer : B.
Answer: (B) 7.2
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
(A) Rs. 1(2/9)
(B) Rs. 2(2/7)
(C) Rs. 2(2/11)
(D) Rs. 2(2/13)
(E) Rs. 2(1/9)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: (B) Rs. 2(2/7)
Question: A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
(A) Rs. 1200
(B) Rs. 1300
(C) Rs. 1500
(D) Rs. 2000
(E) None of these
Rationale: Explanation :
Interest on Rs.3000 at 5% per annum = ( 3000 × 5 × 1) / 100 = Rs. 150
Let his additional investment at 8% = x
Interest on Rs.x at 8% per annum = ( x × 8 × 1 ) / 100 = 2x/25.
To earn 6% per annum for the total, interest = (3000 + x) × 6 × 1/100.
=> 150 + 2x/25 = (3000 + x) × 6 × 1/100.
=> 15000 + 8x = (3000 + x) × 6.
=> 15000 + 8x = 18000 + 6x.
=> 2x=3000.
=> x=1500.
Answer : C
Answer: (C) Rs. 1500
Question: If we have 12 people in a meeting, in how many ways they can sit around a table?
(A) 11*10!
(B) 9*8!
(C) 8*7!
(D) 7*6!
(E) 6*5!
Rationale: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=12
(n-1)!=11!=11*10!
Ans:A
Answer: (A) 11*10!
Question: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
(A) 33
(B) 88
(C) 40
(D) 99
(E) 11
Rationale: 1/8 - 1/x = 1/10
x = 40
Answer: C
Answer: (C) 40
Question: An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 12th member of this sequence?
(A) A)37
(B) B)40
(C) + 13
(D) D)34
(E) + 13
Rationale: Common difference of an arithmetic series is constant.
2p+2-p=4p+3-2p-2
p=1
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Ans:D
Answer: (D) D)34
Question: Evaluate 75 / .05
(A) 1400
(B) 1500
(C) 1505
(D) None of these
(E) 1506
Rationale: Explanation:
75/.05 = 7500/5 = 1500
Option B
Answer: (B) 1500
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 sec. What is the length of the fast train?
(A) 22
(B) 23
(C) 25
(D) 27 7/9
(E) 27
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: Option D
Answer: (D) 27 7/9
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 337
(B) 278
(C) 288
(D) 860
(E) 721
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: (D) 860
Question: What is the remainder when 570 is divided by 6?
(A) 1
(B) 5
(C) 4
(D) 0
(E) 2
Rationale: Explanation:
52 = 25, on division by 6, the remainder is 1.
53 = 125, on division by 6, the remainder is 5.
54 = 625, on division by 6, the remainder is 1.
55 = 3125, on division by 6, the remainder is 5.
Hence, for 5 (2x) on division by 6, the remainder is 1, and for 5(2x-1) on division by 6, the remainder is 5.
Therefore, for 570, on division by 6, the remainder is 1.
ANSWER: A
Answer: (A) 1
Question: a,b,c are positive numbers such that they are in increasing Geometric progression then how many such numbers are there in (loga+logb+logc)/6 =log6
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: given that a,b,c are in gp
so b/a=c/b =>b^2=ac
(loga+logb+logc)/6=log6
=>log(abc)=6*log6
=>log(ac*b)=log(6^6)
=>log(b^3)=log(6^6)
=>b^3=6^6=>b^3=(6^2)^3
=>b=6^2=36
it means a=2,c=18 or a=3 c=12 or a=4 c=9 or a=6 c=6.
hence there are four such numbers
ANSWER:D
Answer: (D) 4
Question: List I: 2, 4, 6, 8 List II: x,2, 4, 6, 8
(A) 7
(B) 5
(C) 9
(D) 11
(E) 13
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(4+6)/2=5.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 5, then x=5.
Answer: B
Answer: (B) 5
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 85 km apart both 3 and 6 hours after start, then find the distance between the two stations.
(A) 255km
(B) 210km
(C) 220km
(D) 180km
(E) 200km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+85+ 85
2(R+S ) = R+S +170
R+S = 170
Hence distance between XY is R+S+ 85 = 170 +85 =255
Answer : A
Answer: (A) 255km
Question: In a series of football matches, the probability that Team P wins a match against Team Q is 1/4 and the probability that the match ends in a draw is 1/6. If the two teams play five matches, what is the probability that all five matches end in a draw?
(A) 1/4436
(B) 1/5546
(C) 1/6656
(D) 1/7776
(E) 1/8886
Rationale: P(5 draws)=(1/6)^5=1/7776
The answer is D.
Answer: (D) 1/7776
Question: For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 40 candles at a distance of 6 feet from the source, what is the intensity of the light at a distance of 30 feet from the source?
(A) 3/10 candles
(B) 1/2 candles
(C) 8/5 candles
(D) 2 candles
(E) 3 candles
Rationale: ANS = 3/10
S= 60k/d^2
At 6 feet
40 = 60k/36 so k = 24
At 30 feet
S = 60 *24/30^2 = 8/5
C
Answer: (C) 8/5 candles
Question: Jemma takes 2 hours to swim the 4 miles from buoy A to buoy B. Tired from her swim, she then continues to buoy C at half her previous speed. If buoy C is 6 miles away from buoy B, how many more hours will pass before Jemma reaches Buoy C?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Time taken for Jemma to reach buoy B is 2 hours.
The distance between the buoys is 4 miles.
Distance travelled/time taken = Average speed
Hence the average speed to travel the distance is 2m/hr
Now, she would have to travel 6 miles .
However as she is tired the speed is half or 1m/hr
Hence, it will take her 6 hours
(Option C)
Answer: (C) 6
Question: The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.470 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
(A) 400
(B) 420
(C) 430
(D) 450
(E) 525
Rationale: Let no. of non- officers be x
15 * 470 + x * 110 = (x + 15) 120
x = 525
E
Answer: (E) 525
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
(A) 42, 33
(B) 42, 36
(C) 44, 33
(D) 44, 36
(E) None of these
Rationale: Explanation :
Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=> (x + 9) = (56/100)(2x + 9)
=> (x + 9) = (14/25)(2x + 9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
Answer : Option A
Answer: (A) 42, 33
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 2700, then his salary per month in rupees is:
(A) 4000
(B) 6000
(C) 18000
(D) 10000
(E) None of these
Rationale: Total expenditure = 40 + 25 + 15 + 5 = 85%
Saving = (100 - 85) = 15%
15/100 × Salary = 2700, Salary = 18000 Rs.
Answer:C.
Answer: (C) 18000
Question: Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 772.
(A) 120 ,122 , 124 ,126
(B) 120 ,122 , 124 ,128
(C) 120 ,121 , 122 ,123
(D) 125 , 127 ,129, 131
(E) None of these
Rationale: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 772 is written as
x + (x + 2) + 4 x + 20 = 772
Solve for x and find all four numbers
x = 125 , x + 2 = 127 , x + 4 = 129 , x + 6 = 131
Answer D
Answer: (D) 125 , 127 ,129, 131
Question: A shepherd had 17 sheep. All but nine died. How many was he left with ?
(A) Nil
(B) 8
(C) 9
(D) 17
(E) 18
Rationale: Explanation:
'All but nine died' means 'All except nine died' i.e. 9 sheep remained alive.
Answer: C
Answer: (C) 9
Question: If s is a positive even integer, and n and m are consecutive integers, then (n - m)^s/(m - n)^s =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: s= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^s)/((m-n)^s)= ((n-m)/(m-n))^s = (-1)^s
Since we are raising the difference of n and m to power s , which is even , the answer will be 1 .
Answer D
Answer: (D) 1
Question: For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. For instance, h(10)= 2x4x6x8x10. What is the greatest prime factor of h(28)+h(30)?
(A) 5
(B) 7
(C) 13
(D) 29
(E) 31
Rationale: h(28)+h(30)
Since h(n) is the product of all even integers from 2 to n, we can say that all the factors of h(28) will be there in h(30)
so we can write the expression as h(28) (1+30)= h(28) *31
31 is the greatest prime factor since all the prime factors in h(28) will be smaller than 31.
E is the answer
Answer: (E) 31
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 77
(B) 30
(C) 108
(D) 66
(E) 12
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108Kmph.Answer:C
Answer: (C) 108
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 38 min, then the slower pipe alone will be able to fill the tank in?
(A) 229
(B) 787
(C) 152
(D) 128
(E) 121
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/38
4/x = 1/38 => x = 152 min.
Answer: C
Answer: (C) 152
Question: What is the unit digit in (4137)^754?
(A) 1
(B) 3
(C) 7
(D) 9
(E) None of these
Rationale: Unit digit in (4137)^754=unit digit in {{(4137)^4}^188 * (4137)^2}=(1*9)=9.
Correct Option: D
Answer: (D) 9
Question: The arithmetic mean of the scores of a group of students in a test was 40. The brightest 10% of them secured a mean score of 60 and the dullest 20% a mean score of 30. The mean score of remaining 70% is?
(A) 25
(B) 30
(C) 40
(D) 42
(E) 48
Rationale: Let the required mean score be x
10*60 + 20*30 + 70*x = 40*100
600+600+70x = 4000
x = 40
Answer is C
Answer: (C) 40
Question: The fraction 878(21/10000) in decimal form is
(A) None of these
(B) 878.0021
(C) 878.00021
(D) 878.021
(E) Cannot be determined
Rationale: Explanation :
878(21/10000) = 878 + (21/10000) = 878 + 0.0021 = 878.0021. Answer : Option B
Answer: (B) 878.0021
Question: There are 280 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
(A) 600
(B) 650
(C) 700
(D) 750
(E) None of these
Rationale: as per question stem 2/5M (Portion of Men employees who are managers) + 280 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+280= 2/5T, or 2/5(T-M)=280, from here we get that T-M=700, that would be total number of female employees and the answer (C)
Answer: (C) 700
Question: If 7a - 3b = 10b + 40 = -12b - 2a, what is the value of 9a + 9b?
(A) -5
(B) -3
(C) 0
(D) 3
(E) 5
Rationale: (i) 7a - 13b = 40
(ii) 2a + 22b = -40
Adding (i) and (ii):
9a + 9b = 0
The answer is C.
Answer: (C) 0
Question: A bag contains 6 black and 4 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/4
(B) 2/5
(C) 1/7
(D) 1/8
(E) 4/3
Rationale: Let number of balls = (6 + 4) = 10.
Number of white balls = 4.
P (drawing a white ball) =4/10=2/5.
Option B.
Answer: (B) 2/5
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] + 5 = f(3x – 6)
(A) 0
(B) 4
(C) 6
(D) 7
(E) 13
Rationale: Answer = C = 6
f(x) = 3x – 5
2*[f(x)] + 5 = f(3x – 6)
2(3x-5) + 5 = 3 (3x-6) - 5
6x - 5 = 9x - 23
x = 6
Answer: (C) 6
Question: Ashok secured average of 76 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
(A) 66
(B) 74
(C) 78
(D) 86
(E) None of these
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 76
Therefore total marks in 6 subjects = 76 * 6 = 456
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 456 – 370 = 86
ANSWER D
Answer: (D) 86
Question: What is the smallest positive integer x such that 66-x is the cube of a positive integer
(A) 5
(B) 7
(C) 47
(D) 9
(E) 2
Rationale: Given 66-x is a perfect cube
so we will take 64 = 4*4*4
66-x = 64
x =66-64 = 2
correct option is E
Answer: (E) 2
Question: Which one of the following is a prime number?
(A) 45
(B) 90
(C) 81
(D) 29
(E) 91
Rationale: 73 is divisible by 1 and itself So, it is a prime number.
D
Answer: (D) 29
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.00 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) s.666
(B) s.1140
(C) s.999
(D) s.1085
(E) s.1020
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.0 = 666
ANSWER:A
Answer: (A) s.666
Question: In a given set of S = {1,2,3,4,5,6,7,8} what is the median of the set S?
(A) 4
(B) 4.5
(C) 5
(D) 3.5
(E) 6
Rationale: median = 4+5 / 2 = 9/2 = 4.5
Answer is B
Answer: (B) 4.5
Question: A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper?
(A) 20%
(B) 25%
(C) 32%
(D) 46.66%
(E) 50%
Rationale: Solution: While buying,
He buys 1100 gram instead of 1000gram.
Suppose he bought 1100 grams for Rs. 1000.
While selling,
He sells only 900 grams when he takes the money for 1 kg.
Now, according to the problem,
he sells at a 8% profit (20% markup, 10% discount).
Hence, his selling price is Rs. 1080 for 900 grams.
Now,
1100grams for Rs. 1000
Hence, 1188 grams for Rs. 1080
Selling: 900 grams for Rs. 1080.
Hence, % profit = 288/900 = 32%.
(using goods left by goods sold formula)
Answer: Option C
Answer: (C) 32%
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) None
Rationale: EXPLANATION
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer C
Answer: (C) 322
Question: If the area of circle is 616 sq cm then its circumference?
(A) 22
(B) 88
(C) 77
(D) 51
(E) 21
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88
Answer: B
Answer: (B) 88
Question: The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?
(A) 55
(B) 44
(C) 66
(D) 60
(E) 12
Rationale: H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.
Answer:D
Answer: (D) 60
Question: The ratio of the radius of two circles is 1: 4, and then the ratio of their areas is?
(A) 1: 16
(B) 1: 6
(C) 1: 9
(D) 1: 3
(E) 1: 2
Rationale: r1: r2 = 1: 4
Πr12: Πr22
r12: r22 = 1: 16
Answer:A
Answer: (A) 1: 16
Question: Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 10.30 am
(B) 10 am
(C) 9 am
(D) 11 am
(E) 12 am
Rationale: Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am
ANSWER:A
Answer: (A) 10.30 am
Question: A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
(A) 1/7
(B) 2/9
(C) 1/12
(D) 4/17
(E) 2/3
Rationale: Total number of balls = 7+2 = 9
n(S) = 9C3 = 9*8*7 / 3*2 = 84
n(E) = 2C2* 7C1 = 7
Probability = 7/84 = 1/12
Answer is C
Answer: (C) 1/12
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 50,000 as total savings, how much has he saved in Public Provident Fund ?
(A) Rs. 20,000
(B) Rs. 30,000
(C) Rs. 60,000
(D) Rs. 90,000
(E) None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (50000 – x) respectively. Then,
1/3x=1/2(50000-x)
=> x/3 + x/2 = 25000
=> 5x/6 = 25000
=> x= 25000 x 6 /5= 30000
Savings in Public Provident Fund = Rs. (50000 – 30000) = Rs. 20000
Answer A
Answer: (A) Rs. 20,000
Question: What is the units digit of the expression 13^27 +1?
(A) 1
(B) 3
(C) 4
(D) 8
(E) 9
Rationale: Power of 3 follows repetition pattern of = 3, 9, 7, 1, 3, 9, 7, 1 ....
Repetition after 4 powers = (3, 9, 7, 1)
13^27 = 27th Power = 24+3
24/4 = 6 (6 repetitions) + 3 = "7"
7+1=8
Answer D
Answer: (D) 8
Question: Two bullet train s 140 m and 170 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
(A) 15.8 sec.
(B) 12.8 sec.
(C) 11.16 sec.
(D) 10.8 sec.
(E) 08.8 sec.
Rationale: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 170) m = 310 m.
Required time = 310x9/250 = 11.16 sec.
ANSWER C
Answer: (C) 11.16 sec.
Question: The equation f= 2y2 + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at f = -5, the equation for l is
(A) + y + 15 = 0
(B) - 3x - 11 = 0
(C) + y - 16.5 = 0
(D) - y - 7 = 0
(E) + y + 13.5 = 0
Rationale: Is optionC: -3f + y -6.5= 0=C
Answer: (C) + y - 16.5 = 0
Question: The captain of a cricket team of 11 members is 28 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 20 years
(B) 21 years
(C) 22 years
(D) 23 years
(E) 25 years
Rationale: Explanation:
Let the average age of the whole team by x years.
11x â€“ (28 + 31) = 9(x -1)
11x â€“ 9x = 50
2x = 50
x = 25
So, average age of the team is 25 years.
Answer E
Answer: (E) 25 years
Question: If the price of 357 apples is Rs.1517.25, what will be the approximate price of 49 dozens of such apples
(A) Rs. 2500
(B) Rs. 2300
(C) Rs. 2200
(D) Rs. 1400
(E) None of these
Rationale: Let the required price be x
More apples, More price(direct proportion)
Hence we can write as
apples357:(49×12)}::1517.25:x
⇒357x = (49 × 12) × 1517.25
⇒x = (49 × 12 × 1517.25)/357 = (7 × 12 × 1517.25)/51
= (7 × 4 × 1517.25)/17 = 7 × 4 × 89.25 ≈ 2500. Answer A
Answer: (A) Rs. 2500
Question: The product S of the first 10 prime numbers is closest to which of the following?
(A) 6.5 x 10^7
(B) 6.5 x 10^8
(C) 6.5 x 10^9
(D) 6.5 x 10^10
(E) 6.5 x 10^11
Rationale: The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667=S
2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.
Answer: C.
Answer: (C) 6.5 x 10^9
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 24 gallons of gasoline?
(A) 190
(B) 284.6
(C) 300
(D) 292
(E) 312
Rationale: so 12.2 * 24 = 292..
IMO option D is correct answer..
Answer: (D) 292
Question: There are two positive numbers in the ratio 4:8. If the larger number exceeds the smaller by 16, then find the smaller number?
(A) 25
(B) 20
(C) 77
(D) 88
(E) 44
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 4x = 16
4x = 16 => x = 4
=> Smaller number = 5x = 20.
Answer: B
Answer: (B) 20
Question: The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 22.51
(B) 22.0
(C) 22.15
(D) 22.17
(E) 22.63
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(18 + 10) = 56 cm Parameter of the square = 56 cm
i.e. 4a = 56
a = 14
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(âˆ)(14)
= 1/2(22/7)(14) = 308/14 = 22 cm to two decimal places
Answer: B
Answer: (B) 22.0
Question: A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 7 for 85 cents. How many were sold at the first rate?
(A) 45
(B) 21
(C) 9
(D) 15
(E) 13
Rationale: This can be solved like a classical mixture problem but numbers are awkward to deal with.
It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 300 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 7.
300 - 45 = 255 => not a multiple of 7 so exclude
300 - 21 = 279 => not a multiple of 7 so exclude
300 -9 = 291 => not a multiple of 7 so exclude
300 - 15 = 285 => not a multiple of 7 so exclude
300 -13=287 => a multiple of 7 so keep
Hence, answer choice 13 is correct.
E
Answer: (E) 13
Question: How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?
(A) 120
(B) 150
(C) 160
(D) 180
(E) 200
Rationale: 8:12 = 2:3
If 240 lrs of the 2nd variety taken then the 1st variety should be taken as 160 lr
ANSWER C
Answer: (C) 160
Question: A bag contains 3 red, 3 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
(A) 5/8
(B) 7/12
(C) 11/16
(D) 17/24
(E) 37/48
Rationale: P(no red balls) = 7/10*6/9*5/8 = 7/24
P(at least one red ball) = 1 - 7/24 = 17/24
The answer is D.
Answer: (D) 17/24
Question: How many integers from 0 to 44, inclusive, have a remainder of 1 when divided by 3 ?
(A) 13
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 43, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so, 43 = 1+(n-1)3
or, (n-1)3 = 42
or, n-1 = 12
or, n = 13
A
Answer: (A) 13
Question: Divide 50 into two parts so that sum of the reciprocal is 1/12 ?
(A) 10,20
(B) 20,20
(C) 30,20
(D) 40,20
(E) 50,20
Rationale: let two no be x,y
x+y=50 ....eq(1)
1/x+1/y=1/12...eq(2)
x+y/xy=1/12(using eq(1))
xy=600
now, (x-y)^2=(x+y)^2 -4xy
using above
x-y=10.....eq(3)
solving eq(1) & eq(2)
x=30 & y=20
ANSWER:C
Answer: (C) 30,20
Question: emblem is coded as 216;
crude is coded as 125
Crickets will be ?
(A) 243
(B) 644
(C) 512
(D) 380
(E) 464
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
Crickets = 8^3 =512
ANSWER:C
Answer: (C) 512