mathewhe/aqua_rat huggingface dataset:
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 4 cups of tea. Last week Mo drank a total of 26 cups of tea and hot chocolate together. If during that week Mo drank 14 more tea cups than hot chocolate cups, then how many rainy days were there last week?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 26 T-C=14 -> T= 20. C=6.
Mo drinks 4 cups of tea a day then number of days that are not rainy = 20/4 = 5
So number of rainy days = 7-5 = 2
A is the answer.
Answer: (A) 2
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) Rs. 8000
(B) Rs. 8900
(C) Rs. 9000
(D) Rs. 9600
(E) Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: (E) Rs. 10000
Question: Carl can wash all the windows of his house in 7 hours. His wife Maggie can wash all the windows in 4 hours. How many hours will it take for both of them working together to wash all the windows?
(A) 2
(B) 2 1/4
(C) 11 6/2
(D) 4 1/2
(E) 5
Rationale: Work hrs=AB/(A+B)= 28/11 =11 6/2
Answer is C
Answer: (C) 11 6/2
Question: If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to decreased by 10 percent, how much would she earn per week?
(A) Rs.415
(B) Rs.325
(C) Rs.352
(D) Rs.315
(E) Rs.425
Rationale: Soln:-
(406/116)90 =315
In this case long division does not take much time.
(406/116)=3.5
3.5*90=Rs.315
ANSWER:D
Answer: (D) Rs.315
Question: Three numbers are in the ratio 3:5:7. The largest number value is 70. Find difference between Smallest & largest number is?
(A) 40
(B) 45
(C) 35
(D) 30
(E) 50
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 70
= The largest number is = 7
= Then 7 parts -----> 70 ( 7 * 10 = 70 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 40 (4 * 10 = 40)
A
Answer: (A) 40
Question: 106 Ã— 106 + 94 Ã— 94 = ?
(A) 20072
(B) 20062
(C) 10072
(D) 20172
(E) 10272
Rationale: Explanation :
(a + b)2 + (a âˆ’ b)2 = 2(a2 + b2)
(Reference : Basic Algebraic Formulas)
1062 + 942 = (100 + 6)2 + (100 âˆ’ 6)2 = 2(1002 + 62) = 2(10000 + 36) = 20072. Answer : Option A
Answer: (A) 20072
Question: A train 110 m long is running with a speed of 40 km/h. In how many seconds will the train pass a man who is running at 4 km/h in the direction opposite to that in which the train is going?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The speed of the train relative to the man = 40 + 4 = 44 km/h.
44000 m/h * 1h/3600 s = (440/36) m/s
(110 m) / (440/36 m/s) = (110 * 36) / 440 = 36/4 = 9 seconds
The answer is D.
Answer: (D) 9
Question: A certain bag contains 100 balls â€” 50 white, 30 green, 8 yellow, 9 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
(A) 0.9
(B) 0.75
(C) 0.6
(D) 0.88
(E) 0.5
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (50 + 30 + 8)/100 = 88/100 = 0.88.
Answer is D
Answer: (D) 0.88
Question: An assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
(A) 68
(B) 69
(C) 70
(D) 71
(E) 72
Rationale: The time to produce the first 60 cogs is 60/90 = 2/3 hours.
The time to produce the next 60 cogs is 60/60 = 1 hour.
The average output is 120 cogs / (5/3) hours = 72 cogs per hour.
The answer is E.
Answer: (E) 72
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 40 Kmph
(B) 52 Kmph
(C) 60 Kmph
(D) 76 Kmph
(E) 80 Kmph
Rationale: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
C)
Answer: (C) 60 Kmph
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
(A) 32%
(B) 34%
(C) 42%
(D) 44%
(E) 54%
Rationale: Explanation:
Let original length = x metres and original breadth = y metres.
Original area =xy m2New Length =120/100x=6/5x
New Breadth =120/100y=6/5y
=>New Area =6/5x∗6/5y
=>New Area =36/25xy
Area Difference=36/25xy−xy
=11/25xy
Increase%=Differnce/Actual∗100
=11xy/25∗1/xy∗100=44%
ANSWER IS D
Answer: (D) 44%
Question: What is the greatest prime factor of 4^17 - 2^30?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: 4^17 - 2^30
=(2^2)^17 - 2^30
= 2^34 - 2^30
= 2^30 (2^4 -1)
= 2^30 * (16-1)
= 2^30 * 15
= 2^30 * 3 * 5
The greatest prime factor is 5.
The answer is C.
Answer: (C) 5
Question: Pipe A can fill a tank in 10 hrs and pipe B can fill it in 8 hrs. If both the pipes are opened in the empty tank.There is an outlet pipe in 3/4 th of the tank. In how many hours will it be fill 3/4th of that tank?
(A) 3 hr
(B) 3.10hr
(C) 3.15 hr
(D) 3.20 hr
(E) 3.30 hr
Rationale: Part filled A in 1 hr= (1/10)
Part filled B in 1 hr= (1/8)
Part filled by (A+B) together in 1 hr=(1/10)+(1/8)=18/80
So, The tank will be full in 80/18 hrs.
Time taken to fill Exact 3/4th of the tank = (80/18) *(3/4) = 3.20 hrs
Answer : D
Answer: (D) 3.20 hr
Question: If a farmer wants to plough a farm field on time, he must plough 160 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
(A) 600
(B) 490
(C) 448
(D) 435
(E) 679
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 160â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
160x=85(x+2)+40
75x=210
x=2.8
So the farmer planned to have the work done in 6 days, and the area of the farm field is 160(2.8)=448 hectares
correct answer C
Answer: (C) 448
Question: A man has Rs. 176 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 33
(B) 60
(C) 75
(D) 90
(E) 95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 176
16x = 176
x = 11.
Hence, total number of notes = 3x = 33.
Answer: Option A
Answer: (A) 33
Question: The number 0.8 is how much greater than 1/2 ?
(A) ½
(B) 3/10
(C) 1/50
(D) 1/500
(E) 2/500
Rationale: let x be the difference
then
.8-1/2=x
8/10-1/2=x
x= 3/10
ans B
Answer: (B) 3/10
Question: Find the value of x in each of the following equation:	[(17.28/x) / (3.6*0.2)] = 2
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: (17.28/x) = 2*3.6*0.2  x = (17.28/1.44) = (1728/14) = 12.
Answer is A.
Answer: (A) 12
Question: Which of these lines in the xy-plane does not contain any point with two negative coordinates?
(A) y = 4x
(B) y = x + 6
(C) y = x^2 - 5
(D) y = x^3 + 3x
(E) y = 2x^4
Rationale: 2x^4 is 0 when x is 0 and positive for all other values of x.
The answer is E.
Answer: (E) y = 2x^4
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 180 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
(A) 280
(B) 320
(C) 360
(D) 420
(E) 480
Rationale: Easy 480 is the answer.
3/4 ( x/2) = 180
x = 180 * 8 /3 = 480.
Answer E
Answer: (E) 480
Question: Three men sit at a table. One dollar is placed in front of each of them. When a buzzer sounds, the first man to touch the money in front of him keeps the money that is in front of him, while the other two receive nothing. If none of the three men touches the money in front of them, then the amount of money doubles for the next round. After three rounds of this activity, what is the maximum amount of money that any one man could receive?
(A) $4
(B) $5
(C) $10
(D) $15
(E) $16
Rationale: The Optimized scenario
After 1st Round - $1. Let nobody touches the amount will double in next round.
After 2nd Round - $2. Let Man A touches it and get$2 or nobody touches
After 3rd Round - $2 Let the same Man A touches it and get another$2.( $4 in case nobody touches in 2nd round).
So, after 3rd round, the maximum amount a man receives is $4.
Answer (A)
Answer: (A) $4
Question: Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 3?
(A) 2/5
(B) 2/7
(C) 33/83
(D) 51/250
(E) 100/249
Rationale: SOLUTION
The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 51/250.
Answer: D
Answer: (D) 51/250
Question: What is x if x + 2y = 20 and y = 5?
(A) A)10
(B) B)8
(C) C)6
(D) D)4
(E) E)2
Rationale: x = 20 - 2y
x = 20 - 10.
x = 10
Answer : A
Answer: (A) A)10
Question: If the price of a certain bond on May 1st was 1/2 the price of the bond on June 1st and the price of the bond on July 1st was 50% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
(A) 50%
(B) 75%
(C) 120%
(D) 133 1/3%
(E) 160%
Rationale: The price on June 1st = 12 (assume);
The price on May 1st = 1/2*12 = 6;
The price on July 1st = 6*1.5 = 9.
The average price of the bond on May 1st and July 1st = (6+9)/2 = 7.5.
The price of the bond on June 1st (12) is 8/5 times (160%) the average price of the bond on May 1st and July 1st.
Answer: E.
Answer: (E) 160%
Question: If x dollars is invested at 12.5 percent for one year and y dollars is invested at 9.5 percent for one year, the annual income from the 12.5 percent investment will exceed the annual income from the 8 percent investment by $60. If $2500 is the total amount invested, how much is invested at 9.5 percent?
(A) a. $1097.83
(B) b. $1231.57
(C) c. $1101.52
(D) d. $1147.72
(E) e. $1352.27
Rationale: 2 equations with 2 unknowns
12.5x / 100 - 9.5y / 100 = 60
and
x + y = 2500
Solving these 2 equations, x =1352.27 and y = 1147.72
Answer D.
Answer: (D) d. $1147.72
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c − a?
(A) 25
(B) 60
(C) 90
(D) 140
(E) It cannot be determined from the information given.
Rationale: -(a + b = 90)
b + c=160
c-a=60
B. 60
Answer: (B) 60
Question: Rs. 6000 is lent out in two parts. One part is lent at 2% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 5:11
(B) 5:6
(C) 5:2
(D) 5:8
(E) 5:2
Rationale: Let the amount lent at 2% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 2/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 1875
Amount lent at 10% = 4125
Required ratio = 5:11
Answer:A
Answer: (A) 5:11
Question: If y/x is an integer, which of the following must also be an integer?
I. xy
II. x/y
III. x
(A) I alone
(B) II alone
(C) None of the above
(D) I and III
(E) III alone
Rationale: Lets take X = 1/6 and Y = 2/3
Then Y/X = 4 which is an integer.
But XY = 1/6 * 2/3 = 1/9 --> Not an integer.
X/Y = 1/6 divided by 2/3 = 1/4 --> Not an integer.
X alone is 1/6. Not an integer.
Hence C. None of the above.
Answer: (C) None of the above
Question: Evaluate permutation
7P7
(A) 5010
(B) 5020
(C) 5030
(D) 5040
(E) None of these
Rationale: Explanation:
nPn=n!
7P7=7*6*5∗4∗3∗2∗1=5040
Option D
Answer: (D) 5040
Question: The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?
(A) 7
(B) 8
(C) 6
(D) 5
(E) 2
Rationale: Explanation:
Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let the ten's and unit's digits be 2x and x respectively.
Then, (10 * 2x + x) - (10x + 2x) = 36
9x = 36
x = 4
Required difference = (2x + x) - (2x - x) = 2x = 8.
Answer: B
Answer: (B) 8
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 77 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
(A) 550
(B) 245
(C) 150
(D) 35
(E) 350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 77, so 0.14*{total} = 77 --> {total} = 550.
Answer: A.
Answer: (A) 550
Question: An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 6 stocks are possible?
--
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
Rationale: 5C2 * 4C2 * 3C2 = 10*6*3 = 180.
Answer: D.
Answer: (D) 180
Question: In a certain code VOLITION is written as UMIEUKRR, MARTINET is written as LYOPJPMX. How is DESTROYS written in this code?
(A) CCPPSQBW
(B) CCPPSQBU
(C) CCPPSQBV
(D) CCPPSQBX
(E) CCPPSQBZ
Rationale: as per the sequence the
ans is D-1 = C
E-2 = C
S-3=P
T-4=P
R+1=S
O+2=Q
Y+3=B
S+4=W
ans is CCPPSQBW
ANSWER:A
Answer: (A) CCPPSQBW
Question: A manufacturer is using glass as the surface for the multi-touch screen of its smartphone. The glass on the manufactured phone has a 6% probability of not passing quality control tests. The quality control manager bundles the smartphone in groups of 10. If that bundle has any smartphone that does not pass the quality control test, the entire bundle of 10 is rejected.
What is the probability that a smartphone bundle that will be rejected by quality control?
(A)  0.25
(B)  .05^10
(C)  1-0.94^10
(D)  1-0.05^10
(E)  0.95^10
Rationale: Find the probability of the opposite event and subtract from 1.
The opposite event is that bundle will NOT be rejected by quality control, which will happen if all 10 phones pass the test, so P(all 10 phones pass test)=0.94^10.
P(at least one phone do not pass the test)=1- P(all 10 phones pass test)=1-0.94^10.
Answer: C.
Answer: (C)  1-0.94^10
Question: If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of is :
(A) 3 M^9
(B) 3 M^2
(C) 3 M^6
(D) 3 M^1
(E) 3 M^7
Rationale: Explanation:
We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.
Now. .
Answer: B) 3 M^2
Answer: (B) 3 M^2
Question: Two pipes can fill a tank in 5 hours and 10 hours. While the 3rd pipe empties the full tank in 10hours. If all the 3 pipes are open in how much time will the tank be filled?
(A) 6hr
(B) 8hr
(C) 2hr
(D) 1hr
(E) 5hr
Rationale: Net part filled in 1 hour = 1/5 + 1/10 - 1/10 = 1/5
The tank will be full in 5 hr
Answer is E
Answer: (E) 5hr
Question: There are 5 candidates in an election and 3 of them are tobe elected. A voter can cast any number of votes but notmore than three. The number of ways in which he can cast his vote is
(A) 5
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: Solution
The voter can cast one or two or three votes. So total number of ways in which he can cast his vote =5C1 + 5C2 + 5C3 = 5 + 10 + 10 = 25. Answer D
Answer: (D) 25
Question: If $30,000 interest is invested in x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
(A) 10,000(x^n)
(B) 30,000n(x/100)
(C) 10,000(1 + x/100)^n
(D) 30,000(x/100)^n
(E) 10,000n(1 + x/100)
Rationale: Principal * no.of years * percentage of interest
Answer : B
Answer: (B) 30,000n(x/100)
Question: Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 7 min
(B) 6 min
(C) 9 min
(D) 10 min
(E) 11 min
Rationale: Due to stoppages, it covers 5 km less.
Time taken to cover 5 km =(5/50)x60 = 6 min
answer : B
Answer: (B) 6 min
Question: If a = (1/6)b and c = 7a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?
(A)  a + 4
(B)  (11/3)a
(C)  (13/3)a
(D)  (4 1/7)a
(E)  (7 1/4)a
Rationale: Official Answer: C
The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.
Were told that a =1/6b, which is equivalent to b = 6a. We can plug that in and simplify the average to:a + 6a + c/3
We also know that c = 7a, which we can plug directly into the average expression:
a + 6a + 7a/3
= 13a/3 = (13/3)a choiceC.
Answer: (C)  (13/3)a
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
(A) 180
(B) 190
(C) 130
(D) 120
(E) 140
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer: Option B
Answer: (B) 190
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
(A) 23/35
(B) 23/36
(C) 23/33
(D) 23/31
(E) 23/32
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Answer: (A) 23/35
Question: Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
(A) 270
(B) 150
(C) 130
(D) 90
(E) 210
Rationale: Let x be the total number of pages in the book, then she finished 2/3*x pages.
Then she has x−2/3*x=1/3*x pages left.
2/3*x−1/3*x=90
1/3*x=90
x=270
So the book is 270 pages long.
Answer is A.
Answer: (A) 270
Question: In a division, divident is 689, divisior is 36 and quotient is 19. Find the remainder.
(A) 4
(B) 3
(C) 2
(D) 5
(E) 6
Rationale: Explanation:
689 = 36 x 19 + r
689 = 684 + r
r = 689 - 684 = 5
Answer: Option D
Answer: (D) 5
Question: The pages of a report are numbered consecutively from 1 to 13. If the sum of the page numbers up to and including page number x of the report is equal to one less than the sum of the page numbers following page number x, then x =
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: sum of the first few numbers =1+2+3+4+5+6+7+8+9 =45
sum of the last few = 10 +11+12+13 =46 page no.9 answer .E
Answer: (E) 9
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 5 days. B can do the work alone in?
(A) 19
(B) 12
(C) 11
(D) 30
(E) 114
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/5
6/x = 1/5 => x = 30
So, B takes 15 hours to finish the work.
Answer: D
Answer: (D) 30
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $4.25 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $21.25m
(B) $25.5m
(C) $106.25m
(D) $127.5m
(E) $153m
Rationale: 2/10*1/6*(total) = 4.25
1/30*(total) = 4.25
(total) = 4.25*30 = 127.5
Answer: D.
Answer: (D) $127.5m
Question: A and B together can do a work in 6 days. If A alone can do it in 15 days. In how many days can B alone do it?
(A) 7
(B) 13
(C) 19
(D) 10
(E) None
Rationale: 1/6 â€“ 1/15 = 1/10
B can do the work in 10 days
Answer: D
Answer: (D) 10
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got?
(A) 55%
(B) 56%
(C) 57%
(D) 58%
(E) 59%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
ANSWER : C
Answer: (C) 57%
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 50 m
(B) 150 m
(C) 200 m
(D) 300 m
(E) None of these
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
ANSWER:B
Answer: (B) 150 m
Question: Distances from you to Man united is written below.
CHELSEA and ARSENAL are 700 kms away
SPURS 1800 kms away
WOLVES 200 kms away
Based on the system , How far should it be to MANCITY ?
(A) 1100 miles.
(B) 3100 miles.
(C) 2100 miles.
(D) 5100 miles.
(E) 4100 miles.
Rationale: Solution:
2100 miles.
Each vowel equivalent to 500 and each consonant equivalent to -200
Answer C
Answer: (C) 2100 miles.
Question: Amar takes as much time in running 18 meters as a car takes in covering 12 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
(A) 6200 m
(B) 2400 m
(C) 300 m
(D) 4300 m
(E) 1200 m
Rationale: B
2400 m
Distance covered by Amar = 18/1.2 (1.6km) = 3/8(1600) = 2400 m
Answer is B
Answer: (B) 2400 m
Question: The sequence of numbers a1, a2, a3, ..., an is defined by an = 1/n - 1/(n+2) for each integer n >= 1. What is the sum of the first 40 terms of this sequence?
(A) (1+1/2) + 1/40
(B) (1+1/2) – 1/42
(C) (1+1/2) – 1/40
(D) (1+1/2) – (1/41 +1/ 42)
(E) (1/41 +1/ 42)
Rationale: The answer would most certainly be[D]. But the question needs a slight modification.n>=1, since the answer does consider a1 under the sum.
The sequence is :
a1 = 1-1/3
a2 = 1/2 - 1/4
a3 = 1/3 - 1/5....
We can observe that the third term in the sequence cancels the negative term in the first. A similar approach can be seen on all the terms and we would be left with 1 + 1/2 from a1 and a2 along with -1/42 and -1/41 from a40 and a39 term which could not be cancelled.
Hence the sum = (1+1/2) – (1/41 +1/ 42)
Answer : D
Answer: (D) (1+1/2) – (1/41 +1/ 42)
Question: A train 120 meters long passes an electric pole in 12 seconds and another train of same length traveling in opposite direction in 8 seconds. The speed of the second train is
(A) 60 Km
(B) 66 Km
(C) 72 Km
(D) 62 Km
(E) 70 Km
Rationale: speed of first train=120/12=10 m/s
let speed of second train be x m/s. As they are approaching each other, relative speed is (10+x) m/s.
distance between each other is 120+120=240 m.
time of crossing each other is 8 sec
=>240/(10+x)=8
=>x=20m/s = 20*18/5 km/hr = 72 kmph
ANSWER:C
Answer: (C) 72 Km
Question: Jack and Jill work at a hospital with 3 other workers. For an internal review, 2 of the 5 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?
(A)  1/3
(B)  1/10
(C)  1/15
(D)  3/8
(E)  2/3
Rationale: 1/5C2=1/10.
Answer: B.
Answer: (B)  1/10
Question: The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
(A) 1:4
(B) 2:3
(C) 3:5
(D) 5:6
(E) 5:7
Rationale: Let the present ages of the two brothers be x and 2x years respectively.
Then, (x - 5)/(2x - 5) = 1/3
3(x - 5) = (2x - 5) => x = 10
Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5
ANSWER:C
Answer: (C) 3:5