mathewhe/aqua_rat huggingface dataset:
Question: If 1,500 is increased by 20%, and then reduced by y%, yielding 1,080, what is y?
(A) 20%
(B) 40%
(C) 60%
(D) 80%
(E) 100%
Rationale: Soln:-
1,500*1.2 = 1,800.
1,800(1 - y/100) = 1,080 --> (1 - y/100) = 0.6 --> y = 40%.
ANSWER:B
Answer: (B) 40%
Question: Working alone, machine X can manufacture 1,000 nails in 10 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
(A) 3 9/17
(B) 5 1/3
(C) 2
(D) 7 1/5
(E) 8 4/7
Rationale: rate of machine x = 1000/10
(1000/10 + y)5=1000
y=500/5=100
100 * t = 1000
t=1000*1/500
C. 2
Answer: (C) 2
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/9%
(B) 16 8/3%
(C) 16 2/3%
(D) 132 2/3%
(E) 16 23/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.20 lacs . How many workers were they?
(A) 220
(B) 400
(C) 500
(D) 560
(E) 590
Rationale: N * 50 = (320000 - 300000) = 20000
N = 20000 / 50
= 400
B
Answer: (B) 400
Question: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent S of the interns report no feelings of tiredness during their shifts?
(A) 6
(B) 14
(C) 19
(D) 20
(E) 81
Rationale: < 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired S= 5 + 14 = 19.
Answer: C.
Answer: (C) 19
Question: Out of 410 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
(A) 120
(B) 150
(C) 100
(D) 140
(E) 220
Rationale: n(A)=325,n(B)=175,n(AuB)=410-50=360.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-360=140.
Answer is D
Answer: (D) 140
Question: Joe invested a certain sum of money in a simple interest bond whose value grew to $310 at the end of 3 years and to $410 at the end of another 5 years. What was the rate of interest in which he invested his sum?
(A) 6%
(B) 7%
(C) 8%
(D) 9%
(E) 10%
Rationale: In 5 years, the value grew $100, so the simple interest was $20 per year.
In 3 years, the total interest was 3*$20 = $60
The principal is $310 - $60 = 250.
The interest rate is $20/$250 = 8%
The answer is C.
Answer: (C) 8%
Question: In an animal behavior experiment, 50 tagged white pigeons and 200 tagged gray pigeons were released from a laboratory. Within one week, 85 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?
(A) 81.4
(B) 82
(C) 82.5
(D) 85
(E) 86.5
Rationale: Weighted mix method is best here....
Ratio is 1:4 for 86:80.5...
So the answer required = 80.5+ (85-80.5)*1/5=80.5+4.5*1/5
80.5+0.9=81.4
A
Answer: (A) 81.4
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?
(A) Rs. 500
(B) Rs. 1000
(C) Rs. 1500
(D) Rs. 2000
(E) NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively. Then 4x - 3x = 1000 ⇔ x = 1000.
∴ B's share = Rs. 2x = Rs. (2x1000) = Rs. 2000.
Answer D
Answer: (D) Rs. 2000
Question: Some of 60%-intensity red paint is replaced with 30% solution of red paint such that the new paint intensity is 40%. What fraction of the original paint was replaced?
(A) 2/3
(B) 1/3
(C) 2/5
(D) 1/2
(E) 1/5
Rationale: Let total paint = 1
Let amount replaced = x
60 (1-x) + 30x = 40
x = 2/3
ANSWER:A
Answer: (A) 2/3
Question: A man purchased 15 pens, 12 books, 10 pencils and 5 erasers. The cost of each pen is Rs.36, each book is Rs.45, each pencil is Rs.8, and the cost of each eraser is Rs.40 less than the combined costs of pen and pencil. Find the total amount spent?
(A) 2388
(B) 2337
(C) 1192
(D) 2827
(E) 1180
Rationale: Explanation:
Cost of each eraser = (36 + 8 -40) = Rs.4
Required amount = 15 * 36 + 12 * 45 + 10 * 8 + 5 * 4
540 + 540 + 80 + 20 = Rs.1180
Answer: E
Answer: (E) 1180
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 75 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.19
(B) 7.17
(C) 7.2
(D) 7.35
(E) 7.11
Rationale: T = (121 + 165)/ (75 + 65) * 18/5
T = 7.35
Answer:D
Answer: (D) 7.35
Question: Walking across campus, a student interviewed a group of students. 35% of the students took a finance class last semester, 45% took a marketing class last semester, and 50% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
(A) 40%
(B) 30%
(C) 25%
(D) 15%
(E) 10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 35 + 45 - {both} + 50
{both} = 30%.
The answer is B.
Answer: (B) 30%
Question: If the cost price of 50 articles is equal to the selling price of 28 articles, then the gain or loss percent is?
(A) 22
(B) 65
(C) 78.57
(D) 33
(E) 25
Rationale: Given that, cost price of 50 article is equal to selling price of 28 articles.
Let cost price of one article = Rs. 1
Selling price of 28 articles = Rs. 50
But Cost price of 28 articles = Rs. 28
Therefore, the trader made profit.\Percentage of profit = 22/28 * 100 = 78.57%
Answer:C
Answer: (C) 78.57
Question: Which of the following numbers is the biggest => [-2/7 , -7/8 , -9/10 , -12/13 , -34/35]
(A) A)-2/7
(B) B)-7/8
(C) C)-9/10
(D) D)-12/13
(E) E)-34/35
Rationale: If we observe all the fractions just differ by one i.e denominator vs numerate.. in such case the biggest will be with large values... here all values are with -ve value...the least value is biggest. i.e. -2/7..
Hence A is correct answer...
Answer: (A) A)-2/7
Question: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
(A) 1/126
(B) 1/120
(C) 1/24
(D) 4/25
(E) 1/2
Rationale: Consider a case when all girls select black marbles...So Girl 1 will chose 1 black marble out of 10..and black marble will be chosen from 5 Black marbles
Girl 1 will have a probability of picking black marble 5/10
Girl 2 will have to pick a black marble out of 4 and total remaining no. of marbles 9=4/9
So we have Probability of all girls selecting black marbles as 5/10*4/9*3/8*2/7*1/6 =1/252
Since Girls can also select white marbles so we will have 2 cases so Probability of girls selecting all same colour marbles is 2*1/252 or 1/126
Ans is A
Answer: (A) 1/126
Question: The cost of 10 kg of mangos is equal to the cost of 24 kg of rice. The cost of 6 kg of flour equals the cost of 2 kg of rice. The cost of each kg of flour is $23. Find the total cost of 4 kg of mangos, 3 kg of rice and 5 kg of flour?
(A) 347.4
(B) 984.4
(C) 877.4
(D) 637.4
(E) 667.4
Rationale: Let the costs of each kg of mangos and each kg of rice be $a and $r respectively.
10a = 24r and 6 * 23 = 2r
a = 12/5 r and r = 69
a = 165.6
Required total cost = 4 * 165.6 + 3 * 69 + 5 * 23
= 662.4 + 207 + 115 = $984.40
B
Answer: (B) 984.4
Question: Which of the following is the lowest positive integer that is divisible by the first 6 positive integer multiples of 5?
(A) 300
(B) 600
(C) 720
(D) 950
(E) 1500
Rationale: The number must be divisible by 5, 2*5, 3*5, 2^2*5, 5^2, and 2*3*5.
The lowest such number is 2^2*3*5^2 = 300.
The answer is A.
Answer: (A) 300
Question: Each of the 59 members in Lourdes school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?
(A) 2
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Each of the 59 members in Lourdes school class is required to sign up for a minimum of one and a maximum of three academic clubs.Total = G1 + G2 + G3 - (# In exactly 2) - 2*(# in 3 sets)
59 = 22+27+28 - (6) - 2x
so, # In 3 sets = 6=C
Answer: (C) 6
Question: What annual installment will discharge a debt of Rs 2,360 due in four years at 12% p.a. simple interest?
(A) 400
(B) 500
(C) 300
(D) 600
(E) None
Rationale: Explanation:
Installments paid at the end of 1st, 2nd, 3rd and 4th years earn a simple interest at 12% p.a. for 3, 2, 1 and 0 years respectively.
Hence the respective installments amount to, (100 + 3 x 12), (100 + 2 x 12), (100 + 1 x 12) and 100, when annual installment is Rs 100.
Hence amount paid is Rs. 136 + Rs 124 + Rs 112 + Rs 100 i.e., Rs 472, when the annual installment is Rs.100
For an amount of Rs 2,360, annual installment = 2,360×100/472=Rs500
Answer B
Answer: (B) 500
Question: Which is greatest in 16 ( 2/3) %, 2/5 and 0.17 ?
(A) 2/3
(B) 0.17
(C) 3/2
(D) 0.71
(E) None of them
Rationale: 16 (2/3)% =[ (50/3)* )1/100)] = 1/6 = 0.166, 2/15 = 0.133. Clearly, 0.17 is the greatest.
Answer is B.
Answer: (B) 0.17
Question: which of the following is the square of an prime number?
(A) 144
(B) 529
(C) 576
(D) 441
(E) 256
Rationale: A prime number is a number greater than 1, whose only two whole-number factors are 1 and itself.
here square root of 529 is 23 which is having only two factor, one and its self.
23 is a prime number
answer is B
Answer: (B) 529
Question: Xavier starts from P towards Q at a speed of 90 kmph and after every 12 mins increases his speed by 20 kmph. If the distance between P and Q is 61km, then how much time does he take to cover the distance?
(A) 52
(B) 48
(C) 44
(D) 40
(E) 36
Rationale: first 12min = 90 *12/60 =18km
2nd 12min = 110*12/60 =22km
3rd 12 min = 130*12/60 = 26 km
TOTAL time 12.3 =36 min
E
Answer: (E) 36
Question: Last year the price per share of Stock N increased by p percent and the earnings per share of Stock N increased by q percent, where p is greater than q. By what percent did the ratio of price per share to earnings per share increase, in terms of p and q?
(A) (p-q)/(100+q) %
(B) (100+q) %
(C) 100*(p-q)/(100+q) %
(D) 100*(p-q) %
(E) p/q%
Rationale: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+p/100) and the new earning is: E*(1 +q/100)
The new P/E is: (1+p/100)P/(1+q/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+p/100)/(1+q/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(p-q)/(100+q) %
Answer : C
Answer: (C) 100*(p-q)/(100+q) %
Question: In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 48, what will be his grade at the end of the third year?
(A) 44
(B) 89
(C) 62
(D) 75
(E) 80
Rationale: Cool question!
There's a lot of information given here, so let's eat slow here.
Joey scores a 48 at the end of his first year. That means that he's currently 24 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).
Now, come next year, or his second year at this psychology school, he's technically 25 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.
Well, his second year is then going to be 25(2) + 24 = 74.
Now let's tackle the main question: what's his grade going to be the third year?
Well, he will be at an age of 26 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (26x2), plus half of his previous year's grade (as calculated for his second year, his grade is 74; therefore, 74/2)
Having said that, the final answer would be 26(2) + 74/2 = 52 + 37 = 89 --> (B)
Answer: (B) 89
Question: Find the odd one out:
125, 106, 88, 76, 65, 58, 53
(A) 33
(B) 88
(C) 26
(D) 18
(E) 222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 88 is the answer.
ANSWER: B
Answer: (B) 88
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 1/2 of the remaining paint. How many gallons of paint has Joe used?
(A) 18
(B) 225
(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 = (1/2)*270 = 135 gallons
Total paint used = 225 gallons.
Option B
Answer: (B) 225
Question: There are 3 numbers A, B and C. If A:B = 5/4, B:C = 4/3,C:D = 3/6, then A:D will be?
(A) 5:6
(B) 3 : 5
(C) 5 : 7
(D) 6 : 11
(E) 5 : 3
Rationale: Sol. A : B = 5 : 4, B : C = 4 : 3, C : D = 3 : 6
∴A∶B∶C∶D= 5 : 4 : 3 : 6.
Thus, A : D = 5 : 6
A
Answer: (A) 5:6
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 20%. Find the decrease percent in the revenue derived from it?
(A) 20%
(B) 18%
(C) 4%
(D) 12%
(E) 14%
Rationale: 100 * 100 = 10000
80 * 120 = 9600
10000------- 400
100 ------- ? = 4%
ANSWER:C
Answer: (C) 4%
Question: The ratio of speed of A and B is 3:4.a definite distance covered by B in 24 minutes.
how much time A take to cover that distance?
(A) 18 minute
(B) 32 minute
(C) 76/7 minute
(D) 40 minute
(E) 44/3 minute
Rationale: ratio of time taken by A and B to cover a distance=1/3:1/4=4:3.
let time taken by A and B are 4x minute and 3x minute respectively.
3x=24;x=8.
hence,time taken by A=(4*8)=32 minute
answer B
Answer: (B) 32 minute
Question: If the area of circle is 850 sq cm then its circumference?
(A) 1719.96 m
(B) 1628.82 m
(C) 1925.23 m
(D) 1432.50 m
(E) 1893.45 m
Rationale: Area of Circle = ∏r2
= 22/7(r2) = 860
= r2 = (860)(7/22)
= r = 273.63
Circumference = 2∏r = (2)(22/7)(273.63)
= 1719.96 m
Answer: A
Answer: (A) 1719.96 m
Question: Whats the probability of getting 5 Sunday(my favorite day) in a 31 day month ?
(A) 3/7
(B) 4/7
(C) 5/7
(D) 6/7
(E) 7/7
Rationale: Solution:
3/7
Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday
Answer A
Answer: (A) 3/7
Question: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?
(A) 3 hrs 15 min
(B) 3 hrs 45 min
(C) 4 hrs
(D) 4 hrs 15 min
(E) None
Rationale: Solution
Time taken by one tap to fill half the tank = 3hrs.
Part filled by the four taps in 1 hour	= (4×1/6)
= 2/3.
Remaining part	= (1 - 1/2)
= 1/2.
Therefore,	‹=› 2/3 : 1/2 :: 1 : x
‹=› (1/2×1×3/2)
‹=› 3/ 4 hrs i.e 45 mins.
So, total time taken = 3 hrs 45 min.
Answer B
Answer: (B) 3 hrs 45 min
Question: If m = 9/25, c = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
(A) c, m, w
(B) c, w, m
(C) m, w, c
(D) w, c, m
(E) w, m, c
Rationale: Answer W - w, m, c
m ~ 1/3
c ~ 1/2
and m+w+c = 1 hence w ~ 1/6
Hence increasing order would be w -> m -> c
Answer E
Answer: (E) w, m, c
Question: A rectangle having length 100 cm and width 40 cm. If the length of the rectangle is increased by fifty percent then how much percent the breadth should be decreased so as to maintain the same area.
(A) 25%
(B) 33.33%
(C) 40%
(D) 75%
(E) None of these
Rationale: Explanation :
Solution: (50/(100+50) * 100)% = 33.33%
Answer : B
Answer: (B) 33.33%
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 3 to 6, and the ratio of flour to baking soda is 5 to 1. If there were 30 more pounds of baking soda in the room, the ratio of flour to baking soda would be 4 to 1. How many pounds of sugar are stored in the room?
(A) 30
(B) 50
(C) 60
(D) 45
(E) 70
Rationale: Sugar:Flour = 3:6 = 1:2 = 5:10
Flour:Soda = 5:1 = 10:2;
Thus we have that Sugar:Flour:Soda = 5x:10x:2x.
Also given that 10x/(2x+30) = 4/1 --> x=60 --> Sugar = 5x = 30.
Answer: A
Answer: (A) 30
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 60/r years. If Pat's parents invested $7,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 20 years later, when Pat is ready for college?
(A)  $20000
(B)  $14000
(C)  $12000
(D)  $10000
(E)  $9000
Rationale: Since investment doubles in 60/r years, then for r=6 it'll double in 60/6=~10 years (we are not asked about the exact amount so such an approximation will do). Thus after 20 years investment will become $7,000*2=$14,000 .
Answer: B
Answer: (B)  $14000
Question: A batsman scored 90 runs which included 4 boundaries and 6 sixes. What percent of his total score did he make by running between the wickets?
(A) 45%
(B) 500/11
(C) 42.22%
(D) 55%
(E) 35%
Rationale: Explanation :
Number of runs made by running,
=>90−(4×4+6×6).
=>90−52
=>38
Hence, the required percentage is:-
=>38/90 *100
=>42.22%
Answer : C
Answer: (C) 42.22%
Question: Find the invalid no.from the following series 15, 16, 34, 105, 424, 2124, 12756
(A) 16
(B) 34
(C) 105
(D) 424
(E) 2124
Rationale: 2nd term = (1st term) * 1 + 1 = 15 *1 + 1 = 16.
3rd term = (2nd term) * 2 + 2 = 16 * 2 + 2 = 34
4th term = (3th term) *3 + 3 = 34 * 3 + 3 = 105
5th term = (4th term) * 4 + 4 = 105 * 4 + 4 = 424
6th term = (5th term) * 5 + 5 = 424 * 5 + 5 = 2125
6th term should 2125 instead of 2124.
E
Answer: (E) 2124
Question: P alone can complete a piece of work in 13 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
(A) 6 (1/4) days
(B) 39/4 days
(C) 7 (3/4) days
(D) 8 (3/4) days
(E) 9 (3/4) days
Rationale: Work done by P alone in one day = 1/13th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/13 of the total) = 1/39 of the total.
Work done by P and Q, working together in one day = 1/13 + 1/39 = 4/39 of the total
They would take 39/4 days to complete the work working together.
ANSWER:B
Answer: (B) 39/4 days
Question: A merchant sells 30 metres of cloth and gains selling price of 10 metres. Find the gain percent.
(A) 15 %
(B) 25 %
(C) 50 %
(D) 75%
(E) 70 %
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% =	10/20*100=50%
Profit of 50 % was made by the merchant.
ANSWER IS C
Answer: (C) 50 %
Question: Two kinds of Vodka are mixed in the ratio 1:5 and 5:1 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
(A) 21%
(B) 20%
(C) 21%18%
(D) 23%
(E) Cannot be determined
Rationale: The profit on the first kind of vodka = x%;
The profit on the second kind of vodka = y%.
When they are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%: (x + 2y)/3 = 10.
When they are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%: (2x + y)/3 = 20.
Solving gives: x = 30% and y = 0%.
After the individual profit percent on them areincreased by 4/3 and 5/3 times respectively the profit becomes 40% and 0%,on the first and te second kinds of vodka, respectively.
If they are mixed in equal ratio (1:1), then the mixture will fetch the profit of (40 + 0)/2 = 20%.
Answer: C
Answer: (C) 21%18%
Question: Find the one which does not belong to that group ?
(A) 22
(B) 83
(C) 33
(D) 49
(E) 11
Rationale: Explanation:
36 = 62, 49 = 72, 64 = 82, 81 = 92 and 100 = 102.
36, 64, 81 and 100 are squares of composite numbers, but not 49.
Answer: B
Answer: (B) 83
Question: A man can row 7 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 3.3
(B) 3.4
(C) 3.5
(D) 3.6
(E) 3.7
Rationale: M = 7
S = 1.2
DS = 7 + 1.2 = 8.2
US = 7 - 1.2 = 5.8
x/8.2 + x/5.8 = 1
x = 3.40.Answer: B
Answer: (B) 3.4
Question: If log 27 = 1.416, then the value of log 9 is:
(A) 0.934
(B) 0.944
(C) 0.954
(D) 0.958
(E) 0.998
Rationale: log 27 = 1.416
log (3cube ) = 1.416
3 log 3 = 1.416
log 3 = 0.472
log 9 = log(3square ) = 2 log 3 = (2 x 0.472) = 0.944.
Answer: Option B
Answer: (B) 0.944
Question: A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
(A) 500
(B) 200
(C) 300
(D) 250
(E) 300
Rationale: Let length of the tunnel = x meter
distance = (800 + x)meter
Time = 1 =1 minute = 60 seconds
Speed = 78 km/hr=78 Ã—5/18 =65/3 m/s
800+x =60 Ã— 65/3
800+ x=1300
x=500
ANSWER: A
Answer: (A) 500
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 40 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 40 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 40 / 10 = 4 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 4 = 24 kms... Answer - D
Answer: (D) 24
Question: Find out the wrong term in the series 3, 6, 18, 108, 1944, 103432
(A) 208646
(B) 300458
(C) 103432
(D) 210546
(E) 209952
Rationale: Explanation:
Each number with in the series is the product of the two numbers that proceed it.
So, if (3 * 6 = 18) , then (108 * 1944 = 209952 ). 209952 should replace 103432.
Answer: E) 209952
Answer: (E) 209952
Question: There are 11 lines in plane. How many intersections (Maximum) can be made?
(A) 55
(B) 60
(C) 65
(D) 70
(E) 75
Rationale: First line will cut all other 10, similarly second will cut 9, and so on
total = 10+9+8+7+6+5+4+3+2+1 = 55
ANSWER:A
Answer: (A) 55
Question: If in coded language
1 = 2
2 = 10
3 = 30
4 = 68
then
5 = ?
(A) 130
(B) 140
(C) 150
(D) 160
(E) 170
Rationale: 1^3 + 1= 2
2^3 + 2= 10
3^3 + 3 = 30
4^3 + 4 = 68
5^3 + 5 = 130
Ans : 130
ANSWER:A
Answer: (A) 130
Question: 2 oranges, 3 bananas and 4 apples cost Rs.15. 3 oranges 2 bananas 1 apple costs Rs.10. what is the cost of 3 oranges, 3 bananas and 3 apples?
(A) 30
(B) 15
(C) 10
(D) 20
(E) 40
Rationale: 2or+3ba+4ap=15--->(1)
3or+2ba+1ap=10---->(2)
(1)+(2)
5or+5ba+5ap=15+10
5(or+ba+ap)=25
or+ba+ap=25/5
or+ba+ap=5
therefore 3or+3ba+3ap===>3(or+ba+ap);
3(5)=15;
ANSWER:B
Answer: (B) 15
Question: In measuring the sides of a rectangle, one side is taken 6% in excess, and the other 5% in deficit. Find the error percent in the area calculated from these measurements.
(A) 0.11%
(B) 0.7%
(C) 0.4%
(D) 0.6%
(E) 0.8%
Rationale: Let x and y be the sides of the rectangle. Then, Correct area = xy.
Calculated area = (53/50) x (19/20) y = (144/143)(xy)
Error In measurement = (144/143)xy- xy = (1/143)xy
Error percentage = [(1/143)xy (1/xy)100] % = (7/10) % = 0.7%.
Answer is B.
Answer: (B) 0.7%