mathewhe/aqua_rat huggingface dataset:
Question: A certain team has 9 members, including Joey. A three-member relay team will be selected as follows: one of the 9 members is to be chosen at random to run first, one of the remaining 8 members is to be chosen at random to run second, and one of the remaining 7 members is to be chosen at random to run third. What is the probability that Joey will be chosen to run second or third?
(A) 1/1320
(B) 1/132
(C) 1/110
(D) 2/9
(E) 1/9
Rationale: Total outcomes= 9*8*7
Favorable Outcomes= 11*1*10 and 11*10*1
P=2*8*7*1/9*8*7
P=2/9
Ans D
Answer: (D) 2/9
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie, Brian
II. Regine
III.Stephanie
(A) I only
(B) II only
(C) III only
(D) I or II only
(E) II, or III only
Rationale: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.
Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.
There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.
Answer: E.
Answer: (E) II, or III only
Question: Gretzky Street begins at Orr Street and runs directly east for 5.6 kilometers until it ends when it meets Howe Street. Gretzky Street is intersected every 350 meters by a perpendicular street, and each of those streets other than Orr Street and Howe Street is given a number beginning at 1st Street (one block east of Orr Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Howe Street. What is the highest-numbered street that intersects Gretzky Street?
(A) 12th
(B) 13th
(C) 14th
(D) 15th
(E) 16th
Rationale: 5.6 km / 350 m = 16.
However, the street at the 5.6-km mark is not 16th Street; it is Howe Street.
Therefore, the highest numbered street is 15th Street.
The answer is D.
Answer: (D) 15th
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
(A) 150
(B) 258
(C) 750
(D) 693
(E) 896
Rationale: Explanation:
Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer:C) 750
Answer: (C) 750
Question: Ten years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
(A) 35
(B) 34
(C) 45
(D) 25
(E) 26
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Ten years ago, P was half of Q in age
=> 2(3x – 10) = (4x – 10)
=> 6x – 20 = 4x – 10
=> 2x = 10
=> x = 5
Answer: Option A
Answer: (A) 35
Question: If the magician is not using a trick deck of cards, what is the possibility that he will draw a Jack or Diamond from a very well-shuffled deck of cards?
(A) 1 in 13
(B) 4 in 13
(C) 1 in 4
(D) 4 in 52
(E) 4 in 12
Rationale: This problem uses the principle of adding fractions with a common denominator. Add the number of suits in the deck to the number of cards in each suit in the deck. Use the denominator of number of cards total in the deck. (4/52 + 13/52 = 17/52). Now subtract the number of Jacks of Diamonds in the deck from you answer. (17/52 - 1/52 = 16/52). Further reduce this fraction. (16/52 = 4/13). Answer is B.
Answer: (B) 4 in 13
Question: A number is said to be prime saturated if the product of all the different positive prime factors of q is less than the square root of q. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95
Rationale: q 96 = 3 * 32 = 3 * 2^5
Answer is D.
Answer: (D) 96
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 20000, then find his savings?
(A) Rs.3600
(B) Rs.4000
(C) Rs.3639
(D) Rs.3632
(E) Rs.3602
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 20000 => x = 4000
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs.4000
Answer: B
Answer: (B) Rs.4000
Question: The bus uses 80 gallons of fuel to fly 320 miles. At this rate, how many gallons of fuel are needed for a 800 mile bus?
(A) 100
(B) 300
(C) 150
(D) 200
(E) 50
Rationale: Number of gallons of fuel per mile = 320 /80 = 4 gallons per mile
Number of gallons of fuel for a 800 mile bus = 800/4= 200
ANSWER:D
Answer: (D) 200
Question: A dish of Babette’s mango surprise consists entirely of mangoes, sunflower seeds, agave nectar, and assorted other fruits. If a serving of the dish contains 8 oz. of mango, 6 oz. of sunflower seeds, and 9 oz. of agave nectar, and the ratio of mangoes to sunflower seeds is halved, what is the ratio of mangoes to the rest of the ingredients in the new serving of the dish?
(A) 1 : 2
(B) 13 : 24
(C) 3 : 6
(D) 5 : 13
(E) It cannot be determined from the information given here.
Rationale: This answer would take too many words to explain, so the best option is E, not enough information.
Answer: (E) It cannot be determined from the information given here.
Question: The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?
(A) 228
(B) 287
(C) 277
(D) 188
(E) 100
Rationale: Explanation:
2C + 3T = 1300 --- (1)
3C + 3T = 1200 --- (2)
Subtracting 2nd from 1st, we get
-C + T = 100 => T - C = 100
Answer:E
Answer: (E) 100
Question: The average age of applicants for a new job is 30, with a standard deviation of 7. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
(A) 8
(B) 14
(C) 15
(D) 18
(E) 30
Rationale: within one standard deviation of the average age means 31 +/- 7
23--30--37
number of dif.ages -23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
total=15
C
Answer: (C) 15
Question: Two trains of length 160 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 100/7 sec
(B) 80/7 sec
(C) 112/7 sec
(D) 120/7 sec
(E) 50/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (160 + 100 + 300)/35
= 560/35 = 112/7 sec.
ANSWER:C
Answer: (C) 112/7 sec
Question: If -3 < x < 0, which of the following must be true?
I. x^5 < x^2
II. x^5 < 2 – x
III. x^4 < x^2
(A) I only
(B) I and II only
(C) II and III only
(D) I and III only
(E) I, II and III
Rationale: I. x^5 < x^2 --> since x is always negative x^5 is always negative and x^2 is always positive therefore x^5 < x^2, so this statement is true.
II. x^5 < 2 – x --> x(x^4+1) < 2 --> negative*positive < 0 < 2, so this statement is also true.
III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -3 < x < 0 is follows that x^2>0): x^2 < 1. Since -3 < x < 0, then x^2 can be greater than 1. Hence, this statement is false.
Answer: B.
Answer: (B) I and II only
Question: In Orange County, one sixth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 140
(B) 155
(C) 160
(D) 168
(E) 175
Rationale: The number must be a multiple of both 6 and 7 so the answer is 168.
The answer is D.
Answer: (D) 168
Question: A man can row his boat with the stream at 6 km/h and against the stream in 2 km/h. The man's rate is?
(A) 1 kmph
(B) 2 kmph
(C) 5 kmph
(D) 7 kmph
(E) 8 kmph
Rationale: DS = 6
US = 2
S = ?
S = (6 - 2)/2 = 2 kmph
Answer: B
Answer: (B) 2 kmph
Question: If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 9, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 58
(C) 31
(D) 22
(E) 13
Rationale: M=9p+1
N=9q+3
We need M+N=9p+1+9q+3=9(p+q)+4
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 6 so
p+q=0 ; M+n = 4
p+q=1 ; M+N = 13
P+q=2 ; M+N = 22
and so on, so basically you get something like - 4,13,22,31,40,..... all the other options were turning up.
Then I directly tried p+q=9 because it was closer to 86 for the first option, i got 85,
So Answer A.
Answer: (A) 86
Question: A cube of side one meter length is cut into small cubes of side 25 cm each. How many such small cubes can be obtained?
(A) 56
(B) 60
(C) 62
(D) 64
(E) 65
Rationale: Along one edge, the number of small cubes that can be cut
= 100/25 = 4
Along each edge 25 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 4 * 4 * 4 = 64
Answer: D
Answer: (D) 64
Question: Sixty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
(A)  60
(B)  80
(C)  100
(D)  120
(E)  140
Rationale: 60% of the members have passed the test, thus 30% have not passed the test.
We also know that 30+12=42 members have not passed the test, thus 0.3*Total=42 --> Total=140.
Answer: E.
Answer: (E)  140
Question: Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 22
(B) 10
(C) 39
(D) 88
(E) 27
Rationale: Explanation:
Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am
Answer: B) 10
Answer: (B) 10
Question: Each of the 59 members in a College 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 a College 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
Answer: (C) 6
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
(A) 20
(B) 21
(C) 12
(D) 22
(E) 24
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage =((14/70)x 100)% = 20%.
ANSWER A
Answer: (A) 20
Question: Twenty-one dots are evenly spaced on the circumference of a circle. How many combinations of three dots can we make from these 21 dots that do not form an equilateral triangle?
(A) 1299
(B) 1305
(C) 1311
(D) 1317
(E) 1323
Rationale: The total number of ways we can choose three dots is 21C3=1330.
We can form seven equilateral triangles from these twenty-one dots.
There are 1330 - 7 = 1323 combinations which do not form an equilateral triangle.
The answer is E.
Answer: (E) 1323
Question: A garrison of 400 men had a provision for 31 days. After 28 days 300 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
(A) 65 days
(B) 45 days
(C) 10 days
(D) 16 days
(E) 12 days
Rationale: 400 --- 31
400 --- 3
100 --- ?
400*3 = 100*x => x =12 days.
Answer: E
Answer: (E) 12 days
Question: Evaluate: 30 - |-x + 6| for x = 10
(A) 16
(B) 26
(C) 36
(D) 46
(E) 56
Rationale: Substitute x by 10 in the given expression and evaluate
30 - |- (10) + 6| = 30 - |-10 + 6|
= 30 - | - 4 | = 30 - 4 = 26
correct answer B)26
Answer: (B) 26
Question: If c is 25% of a and 15% of b, what percent of a is b?
(A)  2.5%
(B)  15%
(C)  25%
(D)  125%
(E)  250%
Rationale: Answer = D
25a/100 = 20b/100
b = 25a/20 = 125a/100 = 125%
Answer: (D)  125%
Question: In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: There are a total of 30 members out of which two do not play either of the two sports... so the number of people of folks which play at least one of the sports mentioned is 28.
Now 17 play badminton and 19 play tennis out of 28.
The way I solved this was:
Badminton: (28 - 17 = 11 People)
Tennis (28 - 19 = 9 People)
Hence, the answer was 9 since it was the smaller number out of the two
ANSWER:C
Answer: (C) 9
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 11 minutes 20 seconds and his sister’s time is currently 9 minutes 36 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
(A) 3%
(B) 5%
(C) 8%
(D) 10%
(E) 15%
Rationale: Bob's time = 680 secs.
His sis' time = 576 secs.
Percent increase needed = (680-576/680) * 100 = 104/640 * 100 = 15%. Ans (E).
Answer: (E) 15%
Question: What is the remainder when 1990990900032 is divided by 32 ?
(A) 16
(B) 8
(C) 4
(D) 2
(E) 0
Rationale: For powers of 2 - A number ending in as many 0s as the exponent of 2 will be divisible by that power of 2.
e.g. 2^4 = 16
A number N ending in four 0s will be divisible by 16.
e.g. 2^5 = 32
A number N ending in five 0s will be divisible by 32.
and so on...
1990990900032 = 1990990900000 + 32
1990990900000 ends in five 0s so will be divisible by 32.
32 is divisible by 32.
So 1990990900032 will be divisible by 32. Remainder will be 0.
Answer (E)
Answer: (E) 0
Question: If 28a+30b+31c=520.
then a+b+c=?.a,b,c are natural numbers
(A) 18
(B) 20
(C) 17
(D) 42
(E) 16
Rationale: have a look on your calender
since,we all knw a year consist of 365 days
february is d only month which has 28 days
4 months in a year has 30 days
and,rest 7 months has 31 days..
so,following d given eq. we can write 28*1 + 30*4 + 31*12..
hence values of a,b and c are 1, 4 and 12 respectively..
a+b+c=17
ANSWER:C
Answer: (C) 17
Question: If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y)
(A) 5 : 6
(B) 7 : 8
(C) 8 : 9
(D) 9 : 10
(E) 11 : 12
Rationale: x : y = 1 : 2 means x/y = 1/2
Now, (2x + 3y) : (x + 4y) = (2x + 3y)/(x + 4y) [Divide numerator and denominator by y.]
= [(2x + 3y)/y]/[(x + 4y)/2] = [2(x/y) + 3]/[(x/y) + 4], put x/y = 1/2
We get = [2 (1/2) + 3)/(1/2 + 4) = (1 + 3)/[(1 + 8)/2] = 4/(9/2) = 4/1 × 2/9 = 8/9
Therefore the value of (2x + 3y) : (x + 4y) = 8 : 9
Answer is C
Answer: (C) 8 : 9
Question: There are 5,480 feet in 1 mile and 12 inches in one foot. How many inches are in a mile?
(A) 5,280 - 12
(B) 5,480*12
(C) 12(5,280)
(D) 12^2(5,280)
(E) 12/5,280
Rationale: 1 feet = 12 inches
1 mile = 5480 feet
1 mile = 5480*12 inches
Ans: B
Answer: (B) 5,480*12
Question: closed cylindrical tank contains 36pi cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base
on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, w hat is the height, in feet, of the
surface of the water above the ground?
(A) 1 ft
(B) 2 ft
(C) 3 ft
(D) 4 ft
(E) 5 ft
Rationale: We know that the volume of cylinder = πr^2h
Given tank height = 4ft.
⇒ π r^2 4 = 36π
⇒ r = 3
So the radius is 3 which means the diameter is 6.
As the cylinder is filled to initially exactly half of the capacity, When this cylinder is placed on its side, Water comes up to the height of the radius.
So water comes up to 3 ft
ANSWER:C
Answer: (C) 3 ft
Question: A 300 m long train crosses a platform in 51 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 287
(B) 350
(C) 828
(D) 277
(E) 550
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/5A = 50/3
3x + 900 = 2550 => x = 550 m.
Answer: E
Answer: (E) 550
Question: Which of the following are orthogonal pairs? a. 3i+2j b. i+j c. 2i-3j d. -7i+j ???
(A) a,b
(B) a,c
(C) b,c
(D) a,d
(E) b,d
Rationale: a. 3i+2j
and
c. 2i-3j
are orthogonal pair.
as the dot product of two vectors is zero;so they are orthogonal.
ANSWER:B
Answer: (B) a,c
Question: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 250 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
(A) 1.46%
(B) 1.93%
(C) 10%
(D) 15%
(E) 19%
Rationale: I think there is a typo in question.
It should have been "By weight Liquid 'X ' makes up..... "
Weight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B
When 250gms of A and 700gms of B is mixed :
Weight of Liquid X = (0.8 * 250)/100 + (1.8* 700)/100 = 14.6gms
% of Liquid X in resultant mixture = (14.6/1000) *100 = 1.46%
A
Answer: (A) 1.46%
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: A drug dealer uses 800gm in place of 1kg to sell his goods. Find his actual % profit or loss, when he sells his article his article on 20% gain on cost price?
(A) 32.5%
(B) 37.5%
(C) 35%
(D) 40%
(E) 50%
Rationale: Selling price of 800gm = 100+20 = $120
Profit = 120-80 = $40
% of profit = 40*100/80 =50 %
Answer is E
Answer: (E) 50%
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 4. If the sum of their ages is 88, what is the difference between the ages of Patrick and Monica?
(A) 22
(B) 48
(C) 45
(D) 72
(E) 18
Rationale: Ages of P and Mi=3x:5x
Ages of Mi and Mo=3x:4x
Rationalizing their ages. ratio of their ages will be 9x:15x:20x
Sum=44x=88
x=2
Difference if ages of Pa and Mo=20x-9x=11x=11*2=22
Answer A
Answer: (A) 22
Question: Which of the following fractions is greater than 1/10?
(A) 1. 12/50
(B) 2. 3/11
(C) 3. 2/9
(D) 4. 4/17
(E) 5. 6/24
Rationale: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
D
Answer: (D) 4. 4/17
Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 70% of the total school population of x students, what is x?
(A) 113
(B) 150
(C) 225
(D) 250
(E) 500
Rationale: 90=x/100*70/100*x=>x^2 = 9*10000/7 = > x = 113
A
Answer: (A) 113
Question: The circumferences of two circles are 132 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 2996 sq m
(B) 2897 sq m
(C) 4312 sq m
(D) 5768 sq m
(E) 8470 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 132 and 2∏l = 352
s = 132/2∏ and l = 352/2∏
Difference between the areas = ∏l^2 - ∏s^2
= ∏{66^2/∏^2 - 132^2/∏^2}
= 66^2/∏ - 132^2/∏
= (66 - 132)(66 + 132)/∏
= (110)(242)/(22/7)
= 8470 sq m
Answer:E
Answer: (E) 8470 sq m
Question: If a and b are negative and positive integers respectively,which of the following options must be positive?
(A) ab
(B) a/b
(C) 2a/b
(D) 4a/b
(E) (a + b)^2
Rationale: A. np
-ve*+ve=-ve
will be negative
B. n/p
-ve/+ve=-ve
C.2a/b
-ve/+ve=-ve
D.4a/b
-ve/+ve=-ve
E.(a + b)^2
will be positive irrespective of the absolute values of x and y
will be positive always
Answer: (E) (a + b)^2
Question: In a kilometer race, A beats B by 60 meters or 15 seconds. What time does A take to complete the race?
(A) 277 sec
(B) 235 sec
(C) 667 sec
(D) 167 sec
(E) 176 sec
Rationale: Time taken by B run 1000 meters = (1000 * 15)/60 = 250 sec.
Time taken by A = 250 - 15 = 235 sec.Answer: B
Answer: (B) 235 sec
Question: Ayesha's father was 48 years of age when she was born while her mother was 32 years old when her brother six years younger to her was born. What is the difference between the ages of her parents?
(A) 22 years
(B) 24 years
(C) 26 years
(D) 28 years
(E) 29 years
Rationale: Mother's age when Ayesha's brother was born = 32 years.
Father's age when Ayesha's brother was born = (48 + 6) years = 54 years.
Required difference = (54 - 32) years = 22 years. Answer: Option A
Answer: (A) 22 years
Question: A train 400 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 277 m
(B) 700 m
(C) 900 m
(D) 187 m
(E) 1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (400 + x)/60 = 65/3
x = 900 m.
Answer:C
Answer: (C) 900 m
Question: HOW MANY LITRES OF PURE ACID ARE THERE IN 8 LITRES OF A20% SOLUTION?
(A) 1.4
(B) 1.5
(C) 1.6
(D) 2.4
(E) NONE OF THESE
Rationale: QUANTITY OF PURE ACID=20% OF 8LITRES= (20/100*8)LITRES=1.6 LITRES.
CORRECT OPTIONS:C
Answer: (C) 1.6
Question: In the decimal expansion of (2/5)^8 what is the eighth digit to the right of the decimal point?
(A)  6
(B)  5
(C)  4
(D)  3
(E)  2
Rationale: Step 1 Convert fraction to decimal with two decimal places 2/5 = 0.40 then convert to scientific number = 4*10^-1
Step 2 Multiply 4^8 by 10^-8
Step 3 4 has the sequence 4, 16, 64
Answer is A
Answer: (A)  6
Question: A and B together can do a work in 5 days. If A alone can do it in 15 days. In how many days can B alone do it?
(A) 10
(B) 99
(C) 7.5
(D) 55
(E) 21
Rationale: 1/5 – 1/15 = 2/15
=> 7.5
Answer: C
Answer: (C) 7.5
Question: Find the average of all the numbers between 6 and 30 which are divisible by 4.
(A) 15
(B) 18
(C) 20
(D) 22
(E) None
Rationale: Sol.
Average = (8+12+16+20+24+28 / 6) = 108 / 6 = 18
Answer B
Answer: (B) 18
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 119.
(A) 2400
(B) 1200
(C) 3600
(D) 4400
(E) 2500
Rationale: Number of odd numbers between 1 and 119 is (119+1)/2=60
Therefore Sum of odd numbers 60*60= 3600
ANSWER: C
Answer: (C) 3600
Question: Consider the word RMTMR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5 letter palindromes.
(A) 14355
(B) 15432
(C) 17576
(D) 18543
(E) 16878
Rationale: The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
C
Answer: (C) 17576
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold $480 kilograms of pears that day, how many kilograms did he sell in the afternoon?
(A) 120
(B) 180
(C) 240
(D) 280
(E) 320
Rationale: 3x=480
x=160
Therefore, the salesman sold 160kg in the morning and 2⋅160=320 kg in the afternoon. So answer is E.
Answer: (E) 320