mathewhe/aqua_rat huggingface dataset:
Question: Manoj borrowed Rs.3900 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
(A) 22877
(B) 5655
(C) 2778
(D) 6787
(E) 1771
Rationale: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3900.3.6/100 = Rs.824.85
27P = 70200 = 82485
P = (82485 + 70200)/27 = 3055 + 2600 = Rs.5655
Answer: B
Answer: (B) 5655
Question: Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 60 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?
(A) 36
(B) 72
(C) 132
(D) 144
(E) 180
Rationale: 1st part: - In 1hr, Bus A covers 30 miles.
Relative speed of bus ABus B is (80-30) = 50mph.
So time required for Bus B to cover the exact distance as A is
50*t = 30
t=3/5 = 36min
2nd part
80*t=2d - B has to cover twice the distance
30*(t+1) = d - A traveled 1hr more and has to travel only only d
so
d/30 - 2d/80 = 1
D=120
T= 3hrs = 180 min
Question asks for +ve difference between part 1 and part 2 in minutes
= 180-36 = 180min
E
Answer: (E) 180
Question: The sum of two numbers is 40 and their product is 350. What will be the sum of their reciprocals?
(A) 4/35
(B) 8/75
(C) 75/4
(D) 75/8
(E) 75/6
Rationale: (1/a)+(1/b)=(a+b)/ab=40/350=4/35
ANSWER:A
Answer: (A) 4/35
Question: A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is:
(A) Rs.50
(B) Rs.60
(C) Rs.80
(D) Rs.90
(E) Rs.100
Rationale: Let C.P. of clock be Rs. x.
Then, C.P. of 90 clocks = Rs. 90x.
[(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40
44x + 60x - 103.5x = 40
0.5x = 40 => x = 80
ANSWER:C
Answer: (C) Rs.80
Question: If p/q = 3/5 , then 2p+q= ?
(A) 12
(B) 11
(C) 13
(D) 15
(E) 16
Rationale: let p=3, q=5 then 2*3+5=11
so 2p+q=11.
ANSWER:B
Answer: (B) 11
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
(A) 299
(B) 277
(C) 266
(D) 992
(E) 188
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
Answer:D
Answer: (D) 992
Question: The sum of the digits of a two-digit number is 12. The difference of the digits is 6. Find the number?
(A) 93
(B) 39
(C) 75
(D) 48
(E) Either (a) or (b)
Rationale: Let the two-digit number be 10a + b
a + b = 12 --- (1)
If a>b, a - b = 6
If b>a, b - a = 6
If a - b = 6, adding it to equation (1), we get
2a = 18 => a =9
so b = 12 - a = 3
Number would be 93.
if b - a = 6, adding it to the equation (1), we get
2b = 18 => b = 9
a = 12 - b = 3.
Number would be 39.
There fore, Number would be 39 or 93.
E
Answer: (E) Either (a) or (b)
Question: X men can do a work in 120 days. If there were 20 men less, the work would have taken 60 days more. What is the value of X?
(A) 60
(B) 77
(C) 26
(D) 66
(E) 281
Rationale: We have M1 D1 = M2 D2
120X = (X - 20)180
=> 2X = (X - 20) 3 => 2X = 3X - 60
=> X = 60
Answer:A
Answer: (A) 60
Question: What number has a 5:1 ratio to the number 10?
(A) 36
(B) 50
(C) 76
(D) 56
(E) 62
Rationale: 5:1 = x: 10
x = 50
Answer: B
Answer: (B) 50
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 11
(B) 30
(C) 99
(D) 88
(E) 61
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: B
Answer: (B) 30
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 (/)
396 11,3,4 (/)
462 11,3 (X)
792 11,3,4 (/)
968 11,4 (X)
2178 11,3 (X)
5184 3,4 (X)
6336 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
B
Answer: (B) 4
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 15
(B) 10
(C) 14
(D) 12
(E) 11
Rationale: 2 * 22/7 * 14 * x = 1056 => x = 12
ANSWER:D
Answer: (D) 12
Question: From a total of 4 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
(A) 16
(B) 36
(C) 60
(D) 120
(E) 240
Rationale: Answer=B=36
No of 4 person committees that can be formed=4C2*4C2=36
Answer B
Answer: (B) 36
Question: A train 650 m long is running at a speed of 81 km/hr. In what time will it pass a bridge 340 m long?
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: Speed = 81 * 5/18 = 45/2 m/sec
Total distance covered = 650 + 340 = 990 m
Required time = 990 * 2/45 = 44 sec
Answer: C
Answer: (C) 44
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 20% less than the price each head sold for the day before.what was the gross profit on this shipment?
(A) $100
(B) $115
(C) $125
(D) $130
(E) $135
Rationale: Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 80% of the previous price: 80/100 * 1/2 = $(2/5)
Total revenue by selling 500 heads = 2/5 * 500 = 200
Total revenue after selling 1500 cabbage heads - 200+500 = $700
Money spent on the purchase: $600
Profit = 700-600 = $100
Ans: A
Answer: (A) $100
Question: A man started a business investing Rs.70,000. Rakhi joined him after six months with an amount of Rs.1,05,000 and Sagar joined them with Rs.1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
(A) 7 : 6 : 10
(B) 12 : 15 : 16
(C) 42 : 45 : 56
(D) cannot be determined
(E) None
Rationale: Solution
Aman : Rakhi : Sagar	=(70,000 x 36):(1,05,000 x 30):(1,40,000 x 24)
= 12 : 15 : 16.
Answer B
Answer: (B) 12 : 15 : 16
Question: The probability of pulling a black ball out of a glass jar is 1/X. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
(A) 1/(XY).
(B) X/Y.
(C) Y/X.
(D) 1/(X+Y).
(E) 1/(X-Y).
Rationale: Let the probability of breaking the jar= n
n*1/X = 1/Y
n= X/Y
B is the answer
Answer: (B) X/Y.
Question: In how many different number of ways 8 boys and 3 girls can sit on a shopa which can accommodate 4 persons?
(A) 7900
(B) 7800
(C) 5200
(D) 6400
(E) None
Rationale: Option 'E'
11p4= 11x10x9x8 = 7920
Answer: (E) None
Question: Marts income is 30 percent more than Tims income and Tims income is 40 percent less than Juans income. What percentage of Juans income is Marts income
(A) 124%
(B) b) 120 %
(C) c) 78 %
(D) d) 80 %
(E) e) 64 %
Rationale: M = (130/100)T
T = (60/100)J
=> M = (78/100)J
Answer C.
Answer: (C) c) 78 %
Question: On a map, 1 inch represents 28 miles. How many X XXinches would be necessary to represent a distance of 383.6 miles?
(A) 5.2
(B) 7.4
(C) 13.7
(D) 21.2
(E) 28.7
Rationale: X inches necessary to represent a distance of 383.6 miles = 383.6/28
= 13.7
Answer C
Answer: (C) 13.7
Question: There are 6 people and 6 chairs. In how many different ways people can occupy the chairs?
(A) 12
(B) 15
(C) 720
(D) 36
(E) 120
Rationale: number of ways =6! = 720
Answer is C
Answer: (C) 720
Question: When two coins are tossed, Find the probability of getting all t ails?
(A) 1/3
(B) 3/4
(C) 1/8
(D) 3/8
(E) P(E) =1/4
Rationale: When two coins are tossed,
S = {HH, HT, TH, TT} where H = Head and T = Tail
Let E = event of getting all tails
Then E = {TT}
so, P(E) = n(E)/n(S) =1/4
Answer: (E) P(E) =1/4
Question: A, B and C start swimming in a pool simultaneously from the same end. To complete 12 laps, A takes 10 minutes, B takes 8 minutes and C takes 6 minutes. What is the ratio of speeds A:B:C?
(A) 3:4:5
(B) 10:15:20
(C) 5:4:3
(D) 4:6:5
(E) 12:15:25
Rationale: The slowest one is A, then comes B and the fastest one is C. So, the the ratio of speeds A:B:C must be in ascending order. Eliminate options C, D, and E.
A's speed (distance)/(time) = 12/10 = 6/5 lap per minute = 10 laps in 10 minute;
B's speed (distance)/(time) = 12/8 = 3/2 lap per minute = 15 laps in 10 minutes;
C's speed (distance)/(time) = 12/6 = 2 lap per minute = 20 laps in 10 minutes/
Therefore, the the ratio of speeds A:B:C is 12:15:20.
Answer: B.
Answer: (B) 10:15:20
Question: A woman complete a journey in 15 hours. She travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
(A) 336 km.
(B) 216 km.
(C) 314 km.
(D) 224 km.
(E) 544 km.
Rationale: 0.5x/21 + 0.5x/24 = 15
--> x/21 + x/24 = 30
--> x = 336 km.
A
Answer: (A) 336 km.
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
(A) 30 days
(B) 25 days
(C) 20 days
(D) 15 days
(E) 10days
Rationale: Explanation :
Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as
Work done by P in 1 day × 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days
Answer : Option B
Answer: (B) 25 days
Question: How many three digit numbers V greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?
(A) 72
(B) 48
(C) 120
(D) 96
(E) 76
Rationale: Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.
Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.
Total possible choice 80 - 8 =72=V
Answer: A.
Answer: (A) 72
Question: Raju age after 55 years will be 5 times his age 5 years back, What is the present age of Raju
(A) 28
(B) 17
(C) 10
(D) 77
(E) 20
Rationale: Clearly,
x+55 = 5(x-5)
<=> 4x = 80 => x = 20
Answer:E
Answer: (E) 20
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 20 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 22
(B) 98
(C) 60
(D) 88
(E) 24
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/20 = 3x => x = 10/3.
So, speed of the faster train = 20/3 = 20/3 * 18/5 = 24 km/hr.
Answer:E
Answer: (E) 24
Question: The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter?
(A) 16500
(B) 16299
(C) 22898
(D) 12929
(E) 12091
Rationale: l=5.5m w=3.75m
area of the floor = 5.5 x 3.75 = 20.625 sq m
cost of paving = 800 x 20.625 = Rs. 16500
Answer: A
Answer: (A) 16500
Question: What is the average of 120, 130, 140, 510, 520, 530, 1115, 1120, and 1125?
(A)  419
(B)  551
(C)  601
(D) 590
(E)  721
Rationale: Add 120, 130, 140, 510, 520, 530, 1115, 1120, and 1125
Grouping numbers together may quicken the addition
sum =5310
5310/9 =590
.D
Answer: (D) 590
Question: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 9 and 39 inclusive.
(A) 351
(B) 384
(C) 410
(D) 424
(E) 450
Rationale: We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 9 to 39, inclusive. We're asked for the SUM of this group.
1) Start with the sum of the smallest and the biggest: 9 + 39 = 48
2) Now look at the 'next smallest' and the 'next biggest': 11 + 37 = 48
Now we have proof that there is no middle term. We have 8 bunches of 48
8(48) = 384
B
Answer: (B) 384
Question: SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS:
(A) 15
(B) 16
(C) 18
(D) 25
(E) NONE OF THESE
Rationale: RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4
SUPPOSE TANYA TAKES X DAYS TO DO THE WORK;
5:4::20:X, X=(4x20/5), X=16 DAYS.
CORRECT OPTION: B
Answer: (B) 16
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18 hours
(B) 37/13 hours
(C) 80/13 hours
(D) 12/5 hours
(E) 30/43 hours
Rationale: Speed downstream = 20 + 5 = 25 kmph.
Time required to cover 60 km downstream
= d/s = 60/25
= 12/5 hours.
Answer: D
Answer: (D) 12/5 hours
Question: A tin of oil was 4/5full.when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. how many bottles of oil can the tin contain?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 90
Rationale: Suppose x bottles can fill the tin completely
Then4/5x-3/4x=6-4
X/20=2
X=40
Therefore required no of bottles =40
ANSWER B
Answer: (B) 40
Question: A can complete the job in 2 hours and B can complete the same job in 4 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
(A) 1/6
(B) 3/10
(C) 1/2
(D) 5/6
(E) 8/9
Rationale: A=1/6
Answer: (A) 1/6
Question: At the end of a business conference the 20 people present all shake hands with each other once. How many handshakes will there be altogether ?
(A) 20
(B) 45
(C) 55
(D) 190
(E) 95
Rationale: number of handshakes = 20C2= 20*19/2 = 190
ANSWER:D
Answer: (D) 190
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 6 pumps work to empty the tank in 1 day?
(A) 8
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: 3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 6 pumps then
48/6=8 hrs.
answer :A
Answer: (A) 8
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 15. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 395
Rationale: Clearly, the numbers are (23 x 13) and (23 x 15).
Larger number = (23 x 15) = 345.
Answer: Option D
Answer: (D) 345
Question: If x*y = xy – 2(x + y) for all integers x and y, then 4* (–3) =
(A) –14
(B) –11
(C) –4
(D) 4
(E) 16
Rationale: 4*(-3) = 4*(-3) - 2 (4 + (-3) ) = -12 -2 = -14
Option (A)
Answer: (A) –14
Question: one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 72 workers in the Palabras bookstore, how many of them have read both books?
(A) 13
(B) 12
(C) 9
(D) 8
(E) 4
Rationale: There are total 72 workers.
one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 18 have read Saramago.
5/8 of the workers have read the latest book by H. Kureishi.
So (5/8) * 72 = 45 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 18 - B have read Saramago but not Kureishi.
So, (18 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
72 = 18 + 45 - B + (18 - B - 1)
B = 4
Answer (E)
Answer: (E) 4
Question: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
(A) $ 280,000
(B) $ 320,000
(C) $ 360,000
(D) $ 450,000
(E) $ 540,000
Rationale: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.
So the amount invested will get doubled thrice.
So, 40000 *2 = 80000
80000*2 = 160000
160000*2 = 320000
Hence, the answer is B.
Answer: (B) $ 320,000
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 4 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
(A) 18 : 35 : 50
(B) 3 : 10 : 10
(C) 9 : 14 : 25
(D) 32 : 35 : 25
(E) None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 3x, 4x and 8x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 4x × 140% :
8x × 125% = 36 : 56 : 100
= 9 : 14 : 25
Answer C
Answer: (C) 9 : 14 : 25
Question: A car finishes a journey in ten hours at the speed of 80 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain?
(A) 8 km/hr
(B) 10 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these
Rationale: Distance covered by the car = 80 × 10 = 800 km
\ Speed = 800⁄8 = 100 km/hr
\ Speed gain = 100 – 80 = 20 km/hr
Answer E
Answer: (E) None of these
Question: If Q is the least common multiple of 90,196, and 300, which of the following is NOT a factor of Q?
(A) 600
(B) 700
(C) 900
(D) 2,100
(E) 4,900
Rationale: IF Q is the least common multiple of 90,196 and 300, which of the following is NOT a factor of Q?
A- 600
B- 700
C- 900
D- 2100
E- 4900
90 = 2 * 3 * 3 * 5
196 = 2 * 2 * 7 * 7
300 = 2 * 2 * 3 * 5 * 5
LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7
(TWO 2, TWO 3, TWO 5, TWO 7)
600 = 2 * 2 * 2 * 3 * 5 * 5
700 = 2 * 2 * 5 * 5 * 7
900 = 2 * 2 * 3 * 3 * 5 * 5
2100 = 2 * 2 * 3 * 5 * 5 * 7
4900 = 2 * 2 * 5 * 5 * 7 * 7=A
Answer: (A) 600
Question: Rectangular Floors X and Y have equal area. If Floor X is 10 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?
(A)  13 1/2
(B)  20
(C)  18 3/4
(D)  21
(E)  24
Rationale: The area of a rectangle is: Area = length x width
We are given that floor X is 10 feet by 18 feet and that floor Y is 9 feet wide. So we can say:
length of X = 10
width of X = 18
width of Y = 9
length of Y = n
We also can say:
Area of Floor X = Area of Floor Y
(length of X)(width of X) = (length of Y)(width of Y)
(10)(18) = 9n
(10)(2) = n
20 = n
Answer B.
Answer: (B)  20
Question: The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit L on the height of vehicles that are allowed to use the tunnel?
(A) 5½ ft
(B) 7½ ft
(C) 8 ½ ft
(D) 9½ ft
(E) 10 ft
Rationale: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.
We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.
Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).
Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).
Finally: AB=8, so the correct answer L is 8 - .5 = 7.5... choose (B)!
Answer: (B) 7½ ft
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (Y + X) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.
(A) 2 only.
(B) 3 only.
(C) 1 only.
(D) 2 and 3 only.
(E) 1, 2 and 3.
Rationale: Statement I is TRUE
Statement II is not TRUE
Statement III is not TRUE
Answer : C
Answer: (C) 1 only.
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 40 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 20
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, A is the answer
Answer: (A) 20
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 80 m and they cross each other in 12 sec, then the speed of each train is?
(A) 24
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (80 + 80)/12 => x = 6.66
Speed of each train = 10 m/sec.
= 6.66 * 18/5 = 24 km/hr.
Answer: Option A
Answer: (A) 24
Question: How many multiples of 4 are there between 4 and 64 ?
(A) 12
(B) 64
(C) 14
(D) 16
(E) 60
Rationale: It should be mentioned whether 4 and 64 are inclusive.
If 4 and 64 are inclusive, then the answer is (64-4)/4+1=16.
If 4 and 64 are NOT inclusive, then the answer is (60-8)/4+1=14.
Since OA is C, then we have NOT inclusive case.
Answer: (C) 14
Question: The simple form of the ratio 2/3:2/5 is?
(A) 5:8
(B) 5:5
(C) 5:9
(D) 5:3
(E) 5:1
Rationale: 2/3 : 2/5 = 10:6 = 5:3
Answer: D
Answer: (D) 5:3
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 6 km per hour and the level part at the rate of 9 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 9 km per hour for the entire route?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 9 km/hour
3D / (D/6 + D/9 + D/V) = 9
1/3 = 1/6 + 1/9 + 1/V
1/V = 1/18 and so V = 18 km/h
The answer is C.
Answer: (C) 18