mathewhe/aqua_rat huggingface dataset:
Question: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many two letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
(A) 2,145
(B) 6,435
(C) 12,100
(D) 2420
(E) 25,740
Rationale: Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All two
2. One symmetry and other two non
4. All the two letters can be arranged in 2 ways
( 11c2+ 11c1 * 15c2) *2
( 11*10/ 2 + 11 * 15 * 14 / 2 ) * 2
2420
IMO option D is the correct answer..
OA please...will correct if I missed anything..D
Answer: (D) 2420
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 988
(C) 773
(D) 562
(E) 277
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Answer: (A) 270
Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?
(A) 750
(B) 387
(C) 237
(D) 198
(E) 121
Rationale: Explanation:
1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer: A
Answer: (A) 750
Question: Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?
(A) -33
(B) 34
(C) -45
(D) -56
(E) 45
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: (A) -33
Question: A child must place 5 different toys in 4 different bins. If any of the toys can go in any of the bins, in how many ways can the child place the toys into the bins?
(A) 6^6
(B) 6^4
(C) 4^5
(D) 4^4
(E) 6^4-4^6
Rationale: there are 4 different bins and each of the toy can go to any of these bins..
so answer 4âˆ—4âˆ—4âˆ—4âˆ—4=4^5
ANSWER:C
Answer: (C) 4^5
Question: 0.1+(0.1)^2+(0.1)^3=
(A) 0.1
(B) 0.111
(C) 0.1211
(D) 0.2341
(E) 0.3
Rationale: Explanation:
0.1+(0.1)^2+(0.1)^3=0.1+0.01+0.001=0.111
Answer: Option B
Answer: (B) 0.111
Question: 3 boys and 7 girls can complete John work in 10 days . But 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
(A) 30 days
(B) 35 days
(C) 40 days
(D) 50 days
(E) 60 days
Rationale: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Answer: (C) 40 days
Question: If u, v, and w are consecutive integers such that u > v > w and the sum of u, v, and w is a multiple of 10, which of the following could be the value of u?
(A) 0
(B) 1
(C) 9
(D) 10
(E) 12
Rationale: We're given a very specific set of restrictions in this prompt:
1) U, V and W are CONSECUTIVE INTEGERS
2) U> V > W
3) U+V+W = a multiple of 10
We're asked which of the 5 answer COULD be the value of U given these restrictions. Rather than staring at the screen or doing layered math, we canbrute forcethe answers until we find one that fits these restrictions..
Answer A: U = 0
In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.
Answer B: U = 1
In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.
Final Answer:
B
Answer: (B) 1
Question: If x^2 + y^2 = 50, then the greatest possible value of y is between
(A) 2 and 3
(B) 4 and 5
(C) 5 and 6
(D) 7 and 8
(E) 9 and 10
Rationale: for the greatest possible value of y^2, we must minimize the value of x^2 i.e. lets say x^2 = 0
then we need to find a number y such that y^2 < 50. 7^2 = 49 and 8^2 = 64 so we can say that the maximum possible value of y can be a little more than 7 hence answer = between 7 and 8
hence D
Answer: (D) 7 and 8
Question: Oak trees line both sides of a street for a length of 5/8 of a kilometer. If there is 16 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?
(A) a)	22
(B) b)	23
(C) c)	38
(D) d)	44
(E) e)	46
Rationale: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.
5/8 of 1 km = 625 m
Lets assume that x trees are planted So equation is
x*1 +(x-1)*16 = 625
Solve for x and we get x = 38, answer is C
Answer: (C) c)	38
Question: One-sixth of the students at a nursery school are 5 years old or older. If 15 students have not yet reached their fourth birthday, and a total of 30 students are not between 4 years old and 5 years old, how many children are in the nursery school?
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: x/6 students are > 5 yrs
15 students are < 4 yrs
x/6+15 = 25
x/6 = 10
x = 60
Answer: C
Answer: (C) 60
Question: The length of the bridge, which a train 100 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 230
(B) 240
(C) 245
(D) 250
(E) 275
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (100 + x)/30 = 25/2 => 2(100 + x) = 750 => x = 275 m.
Answer: Option E
Answer: (E) 275
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with the remaining meal ?
(A) 38 men
(B) 32 men
(C) 34 men
(D) 30 men
(E) None of these
Rationale: Explanation:
There is meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 120 men
So, 50 Children = 120/200 * 50 = 30 men
Option D
Answer: (D) 30 men
Question: Some of 15%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 30%. What fraction of the original paint was replaced?
(A) 1/5
(B) 1/3
(C) 1/2
(D) 3/2
(E) 3/5
Rationale: Let total paint = 1
Let amount replaced = x
15 (1-x) + 25x = 30
x = 3/2
ANSWER:D
Answer: (D) 3/2
Question: 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 2 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
(A) 30
(B) 20
(C) 40
(D) 60
(E) 90
Rationale: Let 1Man does 1unit/hr of work
15M in 21 days of 8hrs will do (15*21*8) units
3W = 2M
1W=(2/3)units/hr
21W with 2hrs a day will take (15*21*8)/(21*2*(2/3)) days
=> 90 Days
ANSWER:E
Answer: (E) 90
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 75 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 48
(B) 30
(C) 26
(D) 23
(E) 12
Rationale: Relative speed = 45 + 75 = 120 km/hr.
120 * 5/18 = 100/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/100 = 30 sec.
Answer:B
Answer: (B) 30
Question: On a certain number line, conditions are x<y<z<u<v and xyzuv>0. Which of the following must be true?
I xy>0 II zu>0 III zu>0
(A) I only
(B) I & II only
(C) III only
(D) II only
(E) II and III only
Rationale: Givenx<y<z<u<v and xyzuv>0.
Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve.
We are given : I xy>0 II yz>0 III uv>0
case 1: x and y can be negative/positive and if they are... we get greater than 0.
case 2: we have zu , then z and u both can be negative/positive and if they are... we get greater than 0.
case 2: we have uv , then z and u both can be negative/positive and if they are... we get greater than 0.
if zu both negative , then de both have to negative in order to get greater than 0. In order to xyzuv>0 , zuv can't be negative else we get -ve value, then we need to have either x or y as negative then ab can't be greater than 0.
so cde have to be positive.
xy > 0 , yz > 0 obviouly v will be positive , since we have information uv> 0 . ( Here we have relationship between cd and uv , where u is common).
Option B.
Answer: (B) I & II only
Question: 5^5 is equal to which of the following?
(A) 3,125
(B) 8,752
(C) 9,660
(D) 5,662
(E) 5,608
Rationale: A is the correct answer. We do not really need to calculate it. The last digit for 5^5 will be 5. Hence A is the correct answer
Answer: (A) 3,125
Question: Running at constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 648
(B) 1800
(C) 2700
(D) 10800
(E) 10900
Rationale: If 6 machines can produce 270 bottles in one minute, 10 machines can produce 270*10/6 bottles in the same time. In 4 minutes, they would produce 4*270*10/6=1800
ANSWER:B
Answer: (B) 1800
Question: A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number G of imported lamps stocked at the store?
(A) 3
(B) 10
(C) 13
(D) 20
(E) 23
Rationale: We want to minimize not maximize the expression,.
G=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
But i'm guessing 123-5x/20 can be written as 123- x/4
if x has to be the greatest multiple of 4 less then 410, then it would be 408.
Hence 123-408/4 --> 123-102 -->21
Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E
Answer: (E) 23
Question: If the positive integer y is divisible by 2, 4, and 8, then which of the following must y be divisible by?
I. 8
II. 31
III. 45
(A) III only
(B) I only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: Answer = B
LCM of 2, 4, 8 = 8
Answer = 8
Answer: B
Answer: (B) I only
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
(A) 9 : 25
(B) 6:25
(C) 3:5
(D) 11:25
(E) 16:25
Rationale: Explanation:
a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22 = 9 : 25
A)
Answer: (A) 9 : 25
Question: Phil’s only source of income comes from his job as a question writer. In this capacity, Phil earns a flat salary of $200 per week plus a fee of $9 for every question that he writes. Every year, Phil takes exactly two weeks of unpaid vacation to visit his uncle, a monk in Tibet, and get inspired for the next year. If a regular year consists of 52 weeks and the number of questions that Phil wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Phil’s median annual income over the past 5 years?
(A) $22,474
(B) $25,673
(C) $27,318
(D) $28,495
(E) $31,227
Rationale: Okay u just need less than one min to answer this question. any odd number greater than 20 means that that last digit must be 1,3,5,7, or 9. 9$ per week for every question. So (odd)(odd) will give odd digit. A and C out. (50 weeks) (200) = 10,000. subtract this amount from option B, D and E and u will find that only option D is divisible by 9 (once 10,000 is subtracted from 28495) so its the right choice..D..
Answer: (D) $28,495
Question: What is the lowest possible common multiple H of 2 distinct integers, each greater than 329?
(A) 330·331
(B) 330^2
(C) 33·331
(D) 660
(E) 330
Rationale: Lowest possible common multiple H of 2 distinct integers will have to be multiple of the number greater than 329...which 330..
so one number will be 330...another one will be 660..
Ans is D.
Answer: (D) 660
Question: A shopkeeper sold an article at $1170 and gained a 20% profit. What was the cost price?
(A) $950
(B) $975
(C) $1000
(D) $1025
(E) $1050
Rationale: Let x be the cost price.
1.2x = 1170
x = 1170/1.2 = 975
The answer is B.
Answer: (B) $975
Question: At present the ratio between the ages of Arun and Deepak is 5:7. After 6years, Arun's age will be 36 years. What is the age of Deepak at present?
(A) 35years
(B) 25years
(C) 42years
(D) 39years
(E) 40years
Rationale: Let the present ages of Arun and Deepak be 5x years and 7x years respectively
5x+6 = 36
5x = 30
x = 6
Deepak's age = 7x = 42years
Answer is C
Answer: (C) 42years
Question: Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $2952400, how many months will it take Joan to pay back her mortgage?
(A) 6
(B) 8
(C) 10
(D) 11
(E) 13
Rationale: Joan starts off with 100 $ .. which is to be tripled every month
Her monthly payments look like this :
100 , 300 , 900 , 2700 ......... Upto 2952400
This can be re written as :
100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 29524
So we have 1 , 3 , 9 , 27 ..... 2652400 in GP
We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)
Therefore to find the Sum of n terms of a GP we use this formula :
Sn = a (1-r^n) / 1 -r
Using this and plugging in the information we get ...
29524 = 1 - 3^n / 1-3 ; 1-3^n / -2
Cross multiplying we get
29524 x -2 = 1- 3^n
- 59048 = 1 - 3^n
- 59049 = - 3 ^n
59049 = 3 ^n (negatives cancel out)
59049 can also be re written as 3 ^ 10
Therefore ; 3 ^10 = 3 ^n
Thus n = 10 (C)
Answer: (C) 10
Question: At a contest with 2,500 participants, 1/2 of the people are aged 10 to 12. Next year, the number of people aged 10 to 12 will increase by 1/5. After this change, what percentage of the total 2,500 people will the 10- to 12-year-olds represent?
(A) 55%
(B) 60%
(C) 50%
(D) 45%
(E) 66%
Rationale: I just wanted to mention a couple of things here:
* this is a pure ratio question; the number 2,500 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/5, we are multiplying it by 1 + 1/5 = 6/5, so the answer here must be (1/2)*(6/5) = 3/5 = 60 %.
Answer : B
Answer: (B) 60%
Question: What leat value must be assigned to * so that the number 63576*2 is divisible by 8?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Solution
The given number is divisible by 8, if the number 6x2 is divisible by 8.
Clearly, the least value of x is 3.
Answer C
Answer: (C) 3
Question: A grocer purchased a quantity of bananas at 3 pounds for $0.50 and sold the entire quantity at 4 pounds for $1.00. How many pounds did the grocer purchase if the profit from selling the bananas was $8.00?
(A)  40
(B)  60
(C)  96
(D)  120
(E)  240
Rationale: Cost price of 1 pound of bananas = 0.5/3 = 1/6
Selling price of 1 pound of bananas = 1/4
Profit per pound = (1/4 - 1/6) = (1/12)
Total profit is given as 8
(1/12)*x = 8
x = 96
Answer: C
Answer: (C)  96
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) Rs.6289
(B) Rs.6298
(C) Rs.6290
(D) Rs.6725
(E) Rs.6708
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs.6725.
Answer: D
Answer: (D) Rs.6725
Question: If 2/(a + 4) = 3/(a - 5), then a = ?
(A) -20
(B) -19
(C) -23
(D) -21
(E) -22
Rationale: Multiply all terms of the given equation by (a - 5)(a + 4), simplify and solve
(a - 5)(a + 4)[ 2/(a + 4) ] = (a - 5)(a + 4) [ 3/(a - 5) ]
2 (a - 5) = 3 (a + 4)
a = -22
correct answer E
Answer: (E) -22
Question: In given series 1, 8, 27, 64, 124, 216, 343 only one number is incorrect. Find out that wrong number
(A) 120
(B) 126
(C) 127
(D) 124
(E) 125
Rationale: The numbers are 1^3=1
2^3=8
3^3=27
4^3=64
5^3=125
etc. So, 124 is wrong
ANSWER:D
Answer: (D) 124
Question: In the coordinate plane, points (x, 1) and (7, y) are on line k. If line k passes through the origin and has slope 1/7, then x - y =
(A) 6
(B) 7
(C) 5
(D) 8
(E) 3
Rationale: Line k passes through the origin and has slope 1/7 means that its equation is y=1/7*x.
Thus: (x, 1)=(7, 1) and (7, y) = (7,1) --> x-y=7-1=6.
Answer: A
Answer: (A) 6
Question: If the 30th january 2003 was thursday, what was the day day on 2nd march, 2003?
(A) sunday
(B) thursday
(C) tuesday
(D) saturday
(E) monday
Rationale: Explanation:
30th january, 2003 was thursday.
So, 6th, 13th, 20th, 27th february were all thursdays.
thus 2nd march, 2003 was 3 days after thursday, i.e. , sunday
Answer: A) sunday
Answer: (A) sunday
Question: When all the students in a school are made to stand in rows of 54, 30 such rows are formed. If the students are made to stand in rows of 45, how many such rows will be formed ?
(A) 12
(B) 36
(C) 38
(D) 28
(E) 11
Rationale: Total number of students = 54 x 30
When arranged in rows of 45, number of rows formed are,
= 36.
Answer: B
Answer: (B) 36
Question: A train 250 m long, running with a speed of 50 km/hr will pass a tree in?
(A) 18sec
(B) 20sec
(C) 25sec
(D) 30sec
(E) 1min
Rationale: Speed = 50 * 5/18 = 125/9 m/sec
Time taken = 250 *9/125 = 18 sec
Answer:A
Answer: (A) 18sec
Question: At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
(A) (54 + 6/11) past 49
(B) (54 + 6/11) past 2
(C) (54 + 6/11) past 7
(D) (54 + 6/11) past 4
(E) (54 + 6/11) past 1
Rationale: 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min
50 min. spaces are gained in min. or
Required time = min. past 4.
Answer: D)
Answer: (D) (54 + 6/11) past 4
Question: In a garden, 26 trees are planted at equal distances along a yard 300 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
(A) 10 metres
(B) 20 metres
(C) 14 metres
(D) 12 metres
(E) 13 metres
Rationale: Between 26 trees, there are 25 gaps
Length of each gap
=300/25
=12
i.e., distance between two consecutive trees =12
Answer: D
Answer: (D) 12 metres
Question: The C.P of 20 books is equal to the S.P of 30 books. Find his gain% or loss%?
(A) 63.33%
(B) 34.33%
(C) 33.33%
(D) 31.33%
(E) 36.33%
Rationale: explanation:
20 CP = 30 SP
30 --- 10 CP loss
100 --- ? => 33.33% loss
Answer: C
Answer: (C) 33.33%
Question: Look at this series: 544, 509, 474, 439, ... What number should come next?
(A) 404
(B) 414
(C) 420
(D) 445
(E) None
Rationale: Explanation: This is a simple subtraction series. Each number is 35 less than the previous number.
Answer: Option A
Answer: (A) 404
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 9 hours of the journey.
(A) 342 km
(B) 352 km
(C) 642 km
(D) 742 km
(E) 382 km
Rationale: The total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in AP whose first term is 30 and last term is 46 = 9/2 [30 + 46] = 342 km.
ANSWER:A
Answer: (A) 342 km
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
(A) 9 min
(B) 8 min
(C) 6 min
(D) 4 min
(E) 5 min
Rationale: Explanation:
Required time =12×24 / 12+24
=12 x 24/36
=24/3 = 8 minutes
Answer: Option B
Answer: (B) 8 min
Question: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the pipe B is turned off after?
(A) 6
(B) 9
(C) 8
(D) 2
(E) 4
Rationale: Let B be turned off after x minutes. Then, part filled by (A + B) in x min + part filled by A in (30 - x) min = 1.
x(2/75 + 1/45) + (30- x) 2/75 = 1
11x + 180 - 6x = 225 => x = 9.Answer:B
Answer: (B) 9
Question: There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total Q of the book?
(A) 3003
(B) 3027
(C) 3024
(D) 3021
(E) 3018
Rationale: First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3
Hence:
P:C:B:T(Total)=Q
6:4:3:13 ----> This means, the Total Number must be a multiple of 13.
Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: (A) 3003
Question: In a triangle, one side is 6 Cm and another side is 8 Cm. which of the following can be the perimeter of the triangle?
(A) 22.
(B) 25.
(C) 30.
(D) 32.
(E) 34.
Rationale: Given : one side is 6 Cm and another side is 8 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 22. Hence A.
Answer: (A) 22.
Question: In a box, there are 6 blue, 7 white and 4 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?
(A) 3/16
(B) 5/16
(C) 8/32
(D) 4/17
(E) 6/17
Rationale: Total number of bulbs = (6 + 7 + 4) = 17.
Let E = event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.
Therefore, P(E)=4/17
ANSWER:D
Answer: (D) 4/17
Question: The length of the bridge, which a train 120 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 10 m
(B) 255 m
(C) 245 m
(D) 19 m
(E) 27 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (120 + x)/30
= 25/2 => 2(120 + x) = 750 => x
= 255 m.
Answer: B
Answer: (B) 255 m
Question: A frog jumps 3 ft comes back 2ft in a day. In how many days it will come out of 30ft deep well
(A) 27
(B) 28
(C) 29
(D) 30
(E) 31
Rationale: A frog jumps 3ft in day and comes back 2ft in night.in how many days it will come out of 30ft deep well?
(3-2)*27 +3*1
total days=28
ANSWER:B
Answer: (B) 28
Question: what is the units digit of the expression 7^75+6?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 7 in power repeats pattern of 4: 7-9-3-1. As 75=4*18+3 then the last digit of 7^75 is the same as the last digit of 7^3, which is 3.
Units digit of 7^75+6 will be: 3 + 6 = 9.
answer is E
Answer: (E) 9
Question: The average runs scored by a batsman in 10 matches is 40. In the next 10 matches the batsman scored an average of 30 runs. Find his average in all the 20 matches?
(A) 31
(B) 35
(C) 88
(D) 13
(E) 12
Rationale: Total score of the batsman in 10 matches = 400.
Total score of the batsman in the next 10 matches = 300.
Total score of the batsman in the 20 matches = 700.
Average score of the batsman = 700/20 = 35.
Answer:B
Answer: (B) 35
Question: The length of a rectangle is twice its breadth. If its length is decreased by 4 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. cm. Find the length of the rectangle.
(A) 10/3cm
(B) 20/3cm
(C) 20cm
(D) 16cm
(E) 14cm
Rationale: Explanation:
Let breadth = x. Then, length = 2x. Then,
(2x - 4) (x + 5) - 2x * x = 75 => 6x - 25 = 75 => x =20/3.
Length of the rectangle = 20/3 cm.
Answer: Option B
Answer: (B) 20/3cm
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 477
(B) 408
(C) 279
(D) 276
(E) 291
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 13 + 21 = 34
T = 12
D = 34 * 12 = 408.Answer: B
Answer: (B) 408
Question: If 36 men can do a piece of work in 25 hours, in how many hours will 12 men do it?
(A) 22
(B) 38
(C) 60
(D) 88
(E) 75
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 12:36 ::25:x \inline \fn_jvn \Leftrightarrow (12 x X)=(36 x 25) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 25}{12}=75
Hence, 12 men can do it in 75 hours.
Answer: E) 75
Answer: (E) 75