mathewhe/aqua_rat huggingface dataset:
Question: The value of 51/4 * (125)0.25 is:
(A) 5
(B) 5(5)
(C) 5√5
(D) √5
(E) None
Rationale: Sol.
51/4 * (125)0.25 = 50.25 * (53)0.25 * 5(3*0.25) = 50.25 * 50.75
= 5(0.25 + 0.75) = 51=5.
Answer A
Answer: (A) 5
Question: Before leaving for his business trip, Chad asks his assistant to choose and pack three shirts from his closet, which currently contains eight shirts. If each shirt is a different color, including one blue shirt and one pink shirt, and the assistant chooses the shirts at random, what is the probability that the pink shirt will be one of the shirts packed but the blue shirt will not?
(A) 3/7
(B) 4/7
(C) 5/14
(D) 11/28
(E) 15/56
Rationale: The total number of ways to choose 3 shirts from 8 is 8C3 = 56
The number of ways to choose a pink shirt plus 2 shirts from 6 is 6C2 = 15
P(a pink shirt but not a blue shirt) = 15/56
The answer is E.
Answer: (E) 15/56
Question: For which of the following does f(x)−f(y)=f(x−y) for all values of x and y?
(A) f(a)=a^2
(B) f(a)=a/2
(C) f(a)=a+5
(D) f(a)=2a−1
(E) f(a)=|a|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. f(x) = x^2 and f(y) = y^2
so L.H.S = x^2 - y^2
and R.H.S = (x-y)^2 ==> x^2 + y^2 -2xy.
so L.H.S not equal to R.H.S
with option 2. f(x) = x/2 and f(y) = y/2
L.H.S = x/2 - y/2 ==> 1/2(x-y)
R.H.S = (x-y)/2
so L.H.S = R.H.S which is the correct answer.
B
Answer: (B) f(a)=a/2
Question: In a group of 100 adults, 40 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
(A) 48
(B) 52
(C) 54
(D) 40
(E) 62
Rationale: 12 left-haded women compose 100-40=60% (or 3/5) of all women, so there are total of 5*12=60 women --> 100-60=40 men.
Answer: D.
Answer: (D) 40
Question: A man, a woman and a boy can together complete a piece of work in 4 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman take to complete the work?
(A) 36days
(B) 32days
(C) 34days
(D) 42days
(E) 49days
Rationale: Explanation:
(1 Man + 1 woman + 1 boy)’s 1day’s work = 1/4
1 man’s 1 day work = 1/6
1boy’s 1 day’s work = 1/18
(1 Man + 1 boy) ‘s 1 day’s work = 1/6 + 1/18 = 2/9
Therefore, 1 woman’s 1 day’s work = 1/4 – 2/9 = 1/36
Therefore, the woman alone can finish the work in 36 days.
Answer: Option A
Answer: (A) 36days
Question: A train is 410 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
(A) 20 seconds
(B) 44 seconds
(C) 40 seconds
(D) 50 seconds
(E) None of these
Rationale: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 410+140 = 550 meter
Time = Distance/speed
=550∗2/25=44seconds
Option B
Answer: (B) 44 seconds
Question: The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then what is the area of the park (in sq. m)?
(A) 153500
(B) 153650
(C) 153600
(D) 153700
(E) 153750
Rationale: Let length =3x km,
breadth =2x km
Distance travelled by the man at the speed of 12 km/hr in 8 minutes =2(3x+2x)=10x
Therefore,12×860=10xx=425 km=160 m
Area =3x×2x=6x2
=6×1602=153600 m2
Answer is C.
Answer: (C) 153600
Question: The C.P of 17 books is equal to the S.P of 20 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 16 2/8% loss
(C) 16 3/3% loss
(D) 36 2/3% loss
(E) 15% loss
Rationale: 17 CP = 20 SP
20 --- 3 CP loss
100 --- ? => 15% loss
Answer:E
Answer: (E) 15% loss
Question: A store reported total sales of $400 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
(A) 2%
(B) 17%
(C) 25%
(D) 65%
(E) 83%
Rationale: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 400 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 400 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(400 – 320)/320] x 100
= 25%.
The answer is C.
Answer: (C) 25%
Question: A person deposits 1/16 of his income as Provident Fund and 1/15 of the remaining as insurance premium. If he spends 5/7 of the balance on domestic needs and deposits an amount of Rs. 50 in the bank, his total income would be
(A) 150
(B) 200
(C) 250
(D) 300
(E) 350
Rationale: (1-(1/16))(1-(1/15))(1-(5/7)) of Income = 50
Hence income = 200
ANSWER:B
Answer: (B) 200
Question: Factor: 5x4y3 â€“ 80y3
(A) A) 5y3(x2 + 4)(x + 2)(x -2)
(B) B) 2y3(x2 + 4)(x + 2)(x -2)
(C) C) 3y3(x2 + 4)(x + 2)(x -3)
(D) D) 3y3(x2 + 4)(x + 3)(x -2)
(E) E) 3y3(x2 + 4)(x + 2)(x -4)
Rationale: 5x4y3â€“ 80y3.
= 5y3(x4 â€“ 16).
= 5y3[(x2)2 - 42].
= 5y3(x2 + 4)(x2 - 4).
= 5y3(x2 + 4)(x2 - 22).
= 5y3(x2 + 4)(x + 2)(x -2).
Answer: (A) 5y3(x2 + 4)(x + 2)(x -2)
Answer: (A) A) 5y3(x2 + 4)(x + 2)(x -2)
Question: Two dice are tossed. The probability that the total score is a prime number is
(A) 1/6
(B) 5/12
(C) 1/2
(D) 7/9
(E) 3/8
Rationale: n(S)=36
E= {(1,1),(1,2), (1,4),….(6,5)}
n(E)=15
P(E)=15/36
=5/12
Option B
Answer: (B) 5/12
Question: The average earning of amechanic for the first 4days of a week is Rs.32 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
(A) s. 10
(B) s. 20
(C) s. 32
(D) s. 40
(E) s. 28
Rationale: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 32 + 4 x 22 -20
= Rs. 196
âˆ´ Average earning = 196/ 7
= Rs. 28
E
Answer: (E) s. 28
Question: The speed of a boat in still water in 37 km/hr and the rate of current is 13 km/hr. The distance travelled downstream in 10 minutes is:
(A) 10.44 km
(B) 10.6 km
(C) 11.4 km
(D) 11.22 km
(E) 8.33 km
Rationale: Explanation:
Speed downstream = (37 + 13) = 50 kmph
Time = 24 minutes = 10/60 hour = 1/6 hour
Distance travelled = Time × speed = (1/6)×50 = 8.33 km
Answer: Option E
Answer: (E) 8.33 km
Question: A salesperson received a commission of 3 percent of the sale price for each of the first 100 machines that she sold and 4 percent of the sale price for each machine that she sold after the first 100. If the sale price of each machine was $10,000 and the salesperson received a $40,000 commission, how many machines did she sell?
(A)  90
(B)  103
(C)  105
(D)  115
(E)  125
Rationale: First 100 machines = 3% commission = 0.03*100*10000 = 30000
Commission from sale of next machines = 40000 - 30000 = 10000
So 25 more machines..
Total = 125 machines
IMO E...
Answer: (E)  125
Question: How many seconds will a 800 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
(A) 48
(B) 36
(C) 26
(D) 11
(E) 18
Rationale: Explanation:
Here distance d = 800 mts
speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s
time t = = 48 sec.
Answer: A
Answer: (A) 48
Question: For any real number x, the operatoris defined as:
(x) = x(4 − x)
If p + 1 =(p + 1), then p =
(A) -2
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: (x) = x(4 − x)
(p + 1) = (p + 1)(4 - p - 1) = (3-p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (3-p)(p+1) = (p + 1)
Or (p + 1) + (p-3)(p+1) = 0
(p + 1)(p-3) = 0
p = -1,p=3
Option E
Answer: (E) 3
Question: Yid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Yid have meant to type?
(A) 10
(B) 16
(C) 21
(D) 24
(E) 27
Rationale: Yid intended to type a seven-digit number Should be 21.
there are two possibilities for placing 2 3s .
case 1: two 3s were missed consecutively. i.e. he typed 33 and it came blank on screen.
-5-2-1-1-5- in this arrangement we can fit 33 in 6 ways . (Six dashes, each dash represent one possible place for placing 33)
case 2: two 3s are not together, i.e. they have one or more digits between them .
-5-2-1-1-5- , in this arrangement
if we place first 3 at first dash i.e. 35-2-1-1-5- then the other 3 can fit into 5 places.
if we place first 3 at second dash i.e. -532-1-1-5- then the other 3 can fit into 4 places.
if we place first 3 at third dash i.e. -5-231-1-5- then the other 3 can fit into 3 places.
if we place first 3 at fourth dash i.e. -5-2-131-5- then the other 3 can fit into 2 places.
if we place first 3 at Fifth dash i.e. -5-2-1-135- then the other 3 can fit into 1 place.
so total 15 ways.
case 2 + case 1 = 6+ 15 = 21 ways
Answer C
Answer: (C) 21
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the 1st and last places?
(A) A)340
(B) B)360
(C) C)256
(D) D)196
(E) E)400
Rationale: Explanation:
The word MEADOWS has 7 letters of which 3 are vowels.
V - - - - - V
As the vowels have to occupy 1st and last places, they can be arranged in the 3C2 i.e., 3 ways. While the consonants and vowel can be arranged among themselves in the remaining 5 places in 5! i.e., 120 ways.
Hence the total ways are 120 * 3 = 360.
B
Answer: (B) B)360
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
(A) 56 kg
(B) 56 kg
(C) 56 kg
(D) 176 kg
(E) 739 kg
Rationale: 25x + 46 = 26(x – 5)
x = 176
Answer:D
Answer: (D) 176 kg
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was
(A) 548
(B) 9674
(C) 2397
(D) 2700
(E) 3000
Rationale: Explanation:
Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
=(45/100*6000)=2700
Answer: D
Answer: (D) 2700
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 16
(B) 17
(C) 10
(D) 19
(E) 15
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x = 5
Deepak's age = 3x = 15 years.
Answer: B
Answer: (B) 17
Question: The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
(A) 7
(B) 2
(C) 4
(D) 5
(E) 1
Rationale: Explanation:
Let the two-digit number be 10a + b
a = b + 2 --- (1)
10a + b = 7(a + b) => a = 2b
Substituting a = 2b in equation (1), we get
2b = b + 2 => b = 2
Hence the units digit is: 2.
Answer:B
Answer: (B) 2
Question: If u > 0, which of the following could be true?
I. u^3 > u^2
II. u^2 = u
III. u^2 > u^3
(A) I only
(B) III
(C) IIIII
(D) All of the above
(E) None of the above
Rationale: 1. u^3 > u^2 Well this is true for all u > +1 (but not for values 0 < u < 1)
2. u^2 = u This is true for only one positive number, 1
3. u^2 > u^3 Again this is true only for values of u such that 0 < u < 1
So the answer is D, since there exists at least one value of u which satisfies the equation/ in equation(s)
Answer: (D) All of the above
Question: A can give B 300 meters start and C 600 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12
(B) 111.67
(C) 428.57
(D) 111.11
(E) 101.12
Rationale: A runs 1000 m while B runs 700 m and C runs 400 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 400)/700 = 571.43 m.
B can give C = 1000 - 571.43 = 428.57 m.
Answer:C
Answer: (C) 428.57
Question: Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true
(A)  y = 1.2 × 10^a, where a is a positive integer.
(B)  y = 1.5 × 10^b, where b is a positive integer.
(C)  y = 1.8 × 10^c, where c is a positive integer.
(D)  y = 2.5 × 10^d, where d is a positive integer.
(E)  y = 2.7 × 10^e, where e is a positive integer.
Rationale: Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option B is correct answer?
Answer: (B)  y = 1.5 × 10^b, where b is a positive integer.
Question: If n = 2.0254 and n* is the decimal obtained by rounding n to the nearest hundredth, what is the value of n* – n?
(A)  -0.0053
(B)  -0.0003
(C)  0.0007
(D)  0.0046
(E)  0.0153
Rationale: n*=2.03
n*-n=2.03-2.0254
0.0046
Answer: D
Answer: (D)  0.0046
Question: A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 35 cents?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 7
Rationale: 0.10(x)+0.35(20-x)=2.5
0.10x+7-0.35x=2.5
so x=18
20-x=2
ans is A
Answer: (A) 2
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony two hours from now?
(A) 77,500
(B) 1,240,000
(C) 2,480,000
(D) 3,720,000
(E) 4,960,000
Rationale: 310,000 × 2 × 2 = 310,000 × 4 = B
Answer: (B) 1,240,000
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 350. The profit percent of the retailer is
(A) 10%
(B) 45.8%
(C) 25%
(D) 52%
(E) None of these
Rationale: Explanation:
cost price = (225 + 15) = 240 sell price = 350
gain = (110/240)*100 = 45.8%. Answer: B
Answer: (B) 45.8%
Question: How many two-digit numbers are there whose remainder when divided by 11 is 1, and whose remainder when divided by 6 is 5?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 2 digit numbers whose remainder when divided by 10 is 1 are
11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91
Out of above , numbers whose remainder when divided by 6 is 5 are
11 , 41 and 71
Answer B
Answer: (B) 4
Question: How much water must be added to a 30 quarts of a 75% acid solution to reduce it to a 15%
solution of acid?
(A) 120 qts
(B) 220 qts
(C) 320 qts
(D) 420 qts
(E) 520 qts
Rationale: I’m adding water, so we have
WATER + WATER = WATER
Starting off with 30 quarts and adding x quarts, we should end up with (30 + x) quarts
30 + x = (30 + x)
The problem describes the solution in terms of acid, we have set it up in terms of water. So, we
have to change the percentages and put them in the problem.
.25(30) + x = .85(30 + x)
Again, we multiply both sides of the equation by 100 to get rid of the decimal point.
25(30) + 100x = 85(30 + x)
750 + 100x = 2550 + 85x
15x = 1800
x = 120 qts
correct answer A
Answer: (A) 120 qts
Question: To be considered grade AF, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AF eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AF eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
(A) 800
(B) 840
(C) 864
(D) 900
(E) 1,080
Rationale: We're asked for the smallest possible mass, so what could the lowest mass be per egg AF? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B.
Answer: (B) 840
Question: If a and b are positive integers such that a/b = 2.14, which of the following must be a divisor of a?
(A) 15
(B) 12
(C) 25
(D) 102
(E) 107
Rationale: 1) A and B are positive INTEGERS
2) A/B = 2.14
A = 214
B = 100
214/100 = 2.14
These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...
A = 107
B = 50
107/50 = 2.14
There is no other way to reduce this fraction, so A must be a multiple of 107 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 107, we have to 'factor-down' 107. This gives us only 107, apart from 1. So this integer MUST be a factor of A. You'll find the match in the answer choices.
Answer: E
Answer: (E) 107
Question: 3639 + 11.95 - x = 3054. Find the value of x.
(A) 407.09
(B) 479.75
(C) 523.93
(D) 596.95
(E) None of these
Rationale: Explanation:
Let 3639 + 11.95 – x = 3054
Then, x = (3639 + 11.95) – 3054
= 3650.95 – 3054
= 596.95
ANSWER: D
Answer: (D) 596.95
Question: The sume of the present ages of a father and his son is 60 years.Six years ago ,father’s ago was five times the age of the son.After 6 years,son’s age will be :
(A) 12 years
(B) 14 years
(C) 18 years
(D) 20 years
(E) None of these
Rationale: Solution
Let the present ages of son and father be x and (60 - x)years recepectively.
Then,(60 -x)-6 =5(x-6) ⇔ 54 -x = 5x - 30 ⇔ 6x = 84 ⇔ x =14.
∴ son's age after 6 years = (x + 6) = 20 years. Answer D
Answer: (D) 20 years
Question: The 200 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT
(A)  4
(B)  20
(C)  50
(D)  40
(E)  90
Rationale: Obviously the number of rows must be a factor of 200. The only option which is not a factor of 200 is E (90).
Answer: E.
Answer: (E)  90
Question: Meena wrote all the numbers from 1 to 49,999 inclusive. How many digits did she write in total?
(A) 154,889
(B) 196,889
(C) 238,889
(D) 250,889
(E) 264,889
Rationale: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-49999=>5*40,000 = 200,000
The answer is 238,889
The answer is C.
Answer: (C) 238,889
Question: On the first day of her vacation, Louisa traveled 160 miles. On the second day, traveling at the same average speed, she traveled 280 miles. If the 160-mile trip took 3 hours less than the 280-mile trip, what was the average speed, in miles per hour?
(A) 40
(B) 45
(C) 46
(D) 48
(E) 50
Rationale: (time)*(rate) = (distance)-->(rate) = (distance)/(time)--> given:(rate) = 160/t =280/(t+3)-->4/t = 7/(t+3)-->4t+12=7t ---->3t= 12 . t= 4 ---->(rate ) = 160/4 = 40
Answer: A
Answer: (A) 40
Question: If d is the standard deviation x, y, and z, what is the standard deviation of x - 5, y - 5, z - 5 ?
(A) d
(B) 3d
(C) 15d
(D) d + 5
(E) d + 15
Rationale: If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case SD won't change as we are subtracting 5 from each term in a set --> SD=d.
Answer: A.
Answer: (A) d
Question: Which of the following CAN be the least common multiple of two positive integers 15 and 30?
(A) 15
(B) 30
(C) 10
(D) 5
(E) 25
Rationale: LCM of 15,30 is 30
Answer : B
Answer: (B) 30
Question: A traveler changes 150 pounds into rupees at the rate of Rs. 7000 for 100 pounds. He spends Rs. 9060 and changes the remaining amount back to pounds at the rate of 100 pounds to Rs. 7200. How many pounds will he get?
(A) 20 pounds
(B) 77 pounds
(C) 66 pounds
(D) 55 pounds
(E) 99 pounds
Rationale: Explanation:
Amount of rupees for exchange of 150 pounds = (150/100)*(7000/1) = Rs. 10,500
Out of these Rs.10,500, traveler spent Rs. 9060
Remaining balance in rupees = 10,500 – 9060 = Rs. 1440
Now these Rs. 1440 are exchanged back to pounds with the rate of 100 pounds for Rs. 7200
Amount in pounds = (1440 * 100) / 7200 = 20 pounds
ANSWER:A
Answer: (A) 20 pounds
Question: If 12/x is an integer and 4/x is an integer, which of the following must be true? I. 4/x is an integer II. 18/x is an integer III. 3/x is an integer
(A) III only
(B) II only
(C) II,III only
(D) I,III only
(E) I only
Rationale: The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 4, GCD of 12 and 4, and if x=4 then ONLY I is true.
Answer: E
Answer: (E) I only
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 180 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 2989
(B) 2765
(C) 6000
(D) 2989
(E) 9772
Rationale: Total production of salt by the company in that year
= 5000 + 5180 + 5360 + .... + 6980 = 72060.
Average monthly production of salt for that year
= 72060/12
= 6005.
Answer:C
Answer: (C) 6000
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $7.90?
(A) 426
(B) 430
(C) 443
(D) 480
(E) 486
Rationale: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 7.9$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 1.9 $ left. so we buy 1 pack of 50 for 1$. We now have 0.9$ left, so we buy 30 individual envelopes. If we add up the numbers, we get 400+50+30=480 envelopes. Answer D
Answer: (D) 480
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 140 m length?
(A) 82.1 sec.
(B) 12.5 sec
(C) 19.1 sec.
(D) 17.1 sec.
(E) 42.1 sec.
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 140 = 250 m.
Required time = 250/20 = 12.5 sec.
Answer: B
Answer: (B) 12.5 sec
Question: If in a given number 5 8 9 4 3 2 7 6 1 4, we interchange the first and the second digits, the third and the fourth, the fifth and the sixth and so on, then counting from the right end, which digit will be sixth?
(A) 3
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: after interchange
8 5 4 9 2 3 6 7 1 4
now count from right
sixth digit be 2
ANSWER:B
Answer: (B) 2
Question: From Mumbai railway station,two Trains A and B start simultaneously from stations 400 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 40 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?
(A)  112
(B)  133
(C)  150
(D)  167
(E)  180
Rationale: Since we know the distance (400) and the combined rate (80), we plug it into the formula:
Distance = Rate * Time
400 = 80 * Time
We can solve for the time they will meet cause we added the rate of Train A and Train B together.
So the time will be 400/80 from dividing 80 on both sides to isolate Time in the equation above.
Time will be 20 hours so now you can plug that in for Train A’s distance.
Distance = Rate * Time
Distance = 40 * 20
Distance = 180 according to answer choice E.
Answer: (E)  180
Question: Mixture of milk & water has been kept in two separate bowl. Ratio of milk to water in one of the bowls is 5 : 1 and that in the other bowl 7 : 2. In what ratio the mixtures of these 2 bowl should be added together so that the quantity of milk in the new mixture may become 80%?
(A) 2:3
(B) 3:4
(C) 4:7
(D) 5:7
(E) 6:7
Rationale: Lett. mixtures of the two containers be added together in the ratio of x
= = [ixoox l00%
Since the percentage quantity ofmilk in the new mixture is SO% — so% (45x + 42y) x 5 4 x 54(x y) 225x 210y 216.3E+216y
9x=6y
x:y=2:3
A
Answer: (A) 2:3
Question: Find out the square of a number which when doubled exceeds its one eighth by 15 ?
(A) 16
(B) 25
(C) 19
(D) 64
(E) 17
Rationale: Let the number be p, then the square will be p^2
According to question:
2p = (p/8) +15
=> 16p = p + 120
=> p = 8
p^2 = 8^2 = 64.
Answer : D
Answer: (D) 64