mathewhe/aqua_rat huggingface dataset:
Question: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 400 feet. What is its area, in square feet?
(A) 76,800
(B) 19,600
(C) 20,000
(D) 20,400
(E) 20,800
Rationale: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.
diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle
using the ratio 3:4:5 for sides, and knowing c = 400, you can deduce the following
a=240
b=320
240x320=76,800
A is the answer.
Answer: (A) 76,800
Question: A man cycles at a rate of 4 kmph. He cycles for 45 minutes and then takes a 15 minute break. Determine the total time taken to cover 12 kms by him.
(A) 4 hours 35 minutes
(B) 4 hours
(C) 3 hours
(D) 3 hours 45 minutes
(E) 4 hours 45 minutes
Rationale: Explanation:
Speed of man = 4kmph
Time for which he cycled = 45 minutes.
Distance covered = speed*time
=> 4*45/60
=> 3km
Total time to cover 3 km = 45 minutes + 15 minutes = 60 minutes = 1 hour
Thus 3 km is covered in 1 hour
Required distance to be covered = 12 km
Beginning from origin point, he covers 9 km in 3 hours taking 15 minutes rest after every 45 minutes. To complete 12 kms he goes another 3 km in 45 minutes.
Thus, total time he takes is 3 hours 45 minutes.
ANSWER D
Answer: (D) 3 hours 45 minutes
Question: An article is sold at certain price. By selling it at 2/3 of its price one losses 10%, find the gain at original price?
(A) 35
(B) 25
(C) 10
(D) 20
(E) 30
Rationale: let the original Selling Price be $x. then now Selling Price = $2x/3, loss=10%
now C.P=$20x/27*27/20x*100)%=35%
Answer A) 35.
Answer: (A) 35
Question: Eight machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 16 days?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 2
Rationale: Rate of one machine = 1 job / (20*8) days
let X = number of machines needed to complete the job in 16 days
1/(8*20) * 16 * X = 1 job
X = 10
10-8= 2
ANSWER: E
Answer: (E) 2
Question: A local bank that has 11 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 11 codes?
(A) 3
(B) 11 ( 2 integers 4 codes)
(C) 5
(D) 6
(E) 7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Total = 16 Codes. Enough. Answer: B
4 integers create 11 codes.
Answer: (B) 11 ( 2 integers 4 codes)
Question: The price of a coat in a certain store is $500. If the price of the coat is to be reduced by $400, by what percent is the price to be reduced?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 80%
Rationale: price of a coat in a certain store = $500
the price of the coat is to be reduced by $400
% change = (Final Value - Initial Value)*100 / Initial Value
% Reduction= (Reduction in Price)*100 / Initial Value
i.e. % Reduction= (400)*100 / 500 = 80%
Answer: Option E
Answer: (E) 80%
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 4% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
(A) 22.04%
(B) 26.12%
(C) 28%
(D) 16.25%
(E) 30%
Rationale: Per quarter, interest = 4% So for a year, interest = 16% Due to quarter cumulation, effective yield (YTM) would be slight higher than 16.25% Answer = 16.25% =ANSWER:D
Answer: (D) 16.25%
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is?
(A) 20%
(B) 80%
(C) 90%
(D) 22%
(E) 24%
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%.Answer: A
Answer: (A) 20%
Question: The marks obtained by Vijay and Amith are in the ratio 8:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 12:5
(B) 12:1
(C) 6:5
(D) 12:2
(E) 6:3
Rationale: 8:5
3:2
-------
24:15:10
24:10
12:5
Answer: A
Answer: (A) 12:5
Question: Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 60 percent carbonated water, what percent of the volume of the mixture is P?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: 60% is 20%-points below 80% and 5%-points above 55%.
So the ratio of solution P to solution Q is 1:4.
Mixture P is 1/5 = 20% of the volume of mixture PQ.
The answer is A.
Answer: (A) 20%
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
(A) 2 PM
(B) 1 PM
(C) 7 PM
(D) 5 PM
(E) 8 PM
Rationale: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer:D
Answer: (D) 5 PM
Question: The average age of twenty four boys in a class and the teacher is 15. If the teacher age is excluded, the average reduces to 14. What is the techer's age?
(A) 41
(B) 36
(C) 32
(D) 39
(E) 38
Rationale: 25*15-24*14= 39
ANSWER:D
Answer: (D) 39
Question: Three candidates contested in an election and received 4136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
(A) 45%
(B) 49%
(C) 50%
(D) 51%
(E) 62%
Rationale: Total number of votes polled = 4136+7636+11628 = 23400
Required percentage = 11628*100/23400 = 50%
Answer is C
Answer: (C) 50%
Question: A student has 7 trousers and 11 shirts. In how many different ways can the student select a trouser and a shirt?
(A) 68
(B) 77
(C) 86
(D) 95
(E) 104
Rationale: The student can select one trouser in 7 ways.
The student can select one shirt in 11 ways.
The number of ways to select one trouser and one shirt is 7 * 11 = 77 ways
The answer is B.
Answer: (B) 77
Question: If it is a 3x3 matrix, for which elements in first row are (V, 50, W), second row (196,X, Y)and in third row are (269, Z, 123).It is given that the sum of the numbers in each row, column, diagonal are same. Then find the value of (Y + Z).
(A) 1012
(B) 1011
(C) 1212
(D) 1122
(E) 1021
Rationale: v 50 w
196 x y
269 z 123
in 1st row and 1st column
v+196+269=v+50+w
w=415
Again, in 2nd column and 3rd row
50+x+z=269+z+123
x=342
As sum of each row column and diagonal are same.
So, 269+342+415=1026
415+y+123=1026
y=488
269+z+123=1026
z=634
y+z=488+634=1122
ANSWER:D
Answer: (D) 1122
Question: Ross has 320 shirts, 3/4 of the shirts are green and 1/10 is without buttons. Therefore Ross has between ___ and ___ shirts with buttons that are not green.
(A) 48 ; 80.
(B) 49 ; 80.
(C) 50 ; 80.
(D) 51 ; 80.
(E) 52 ; 80.
Rationale: Total shirts = 320
Green shirts = 3/4*320 = 240, Non green shirts = 80
Shirts without button = 1/10*320 = 32, shirts with button = 288
Required: Range of shirts with buttons that are not green.
Maximum non green shirts with buttons = number of non green shirts = 80
Minimum non green shirts with buttons (All without button shirts are non green) = Non green shirts - shirts without button = 80 - 32 = 48
Hence the range would be (48, 80)
Correct Option: A
Answer: (A) 48 ; 80.
Question: If 1^3 + 2^3 + 3^3 +......+ 10^3 = 516 then the value of 2^3 + 4^3 + 6^3 + ..... + 20^3 is
(A) 1032
(B) 1040
(C) 1048
(D) 1050
(E) 1052
Rationale: 2(13 + 23 + 33 + ---------- + 103)
2 × 516 = 1032
A
Answer: (A) 1032
Question: If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
6 – 9 + 8 × 3 ÷ 20 =
(A) 6
(B) 10
(C) 12
(D) -2
(E) 8
Rationale: B 10
Answer: (B) 10
Question: Two pillars are standing side-by-side. One pillar, which is 6 feets tall, casts a shadow that is 12 feets long. The other pillar is 4 feets tall. Compute, in feets, the length of the shadow that
the shorter pillar casts.
(A) 8
(B) 10
(C) 12
(D) 16
(E) 20
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
6/12 = 4/x and x = 8 .
correct answer A
Answer: (A) 8
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
(A) 43
(B) 30
(C) 35
(D) 45
(E) 50
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
ANSWER A
Answer: (A) 43
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/8
(B) 3/4
(C) 3/5
(D) 3/9
(E) 3/1
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: (B) 3/4
Question: A family made a down payment of $20 and borrowed the balance on a set of encyclopedias that cost $500. The balance with interest was paid in 24 monthly payments of $25 each. The amount of interest paid was what percent of the amount borrowed?
(A)  16%
(B)  25%
(C)  24%
(D)  26%
(E)  20%
Rationale: borrowings = 500-20 = 480
total pmt = 24x25 = 600
so int = 600 - 480 = 120
interest in terms of borrowing = 120/480 = 25%
Answer is B
Answer: (B)  25%
Question: 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability K that one more throw to this series will increase the mean score?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability K is 1/2.C
Answer: (C) 1/2
Question: Define e* by the equation e* = π-e. Then ((−π)*)* =
(A)  −2π
(B)  -1
(C)  −π
(D)  2π
(E)  4π
Rationale: for e* f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π=C
Answer: (C)  −π
Question: A group of 13 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
(A)  E/(12 - n)
(B)  (12 - n)/E
(C)  E/[12(12-n)]
(D)  (12-n)E/(12n)
(E)  nE / [13(13-n)]
Rationale: total cost =E
no of people willing to participate initially =13
initial cost for each =E/13
when n people decided not to participate
Cost for each =E/13-n
E
Answer: (E)  nE / [13(13-n)]
Question: Which of the following fractions can be written as the difference of reciprocals of two consecutive integers
(A) 1/24
(B) 7/30
(C) 1/42
(D) 13/56
(E) 1/73
Rationale: Difference of reciprocals means 1 has to be in the numerator;
So option BD can be ignored
For option A, BE, we require to search two consecutive numbers whose product is the denominator
24 = 4 * 6 ......... Ignore
42 = 6* 7 ........ Answer
73 = 6 * 9 ................ Ignore
Answer = C
Answer: (C) 1/42
Question: A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 197 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
(A) 9801
(B) 10,000
(C) 14,400
(D) 12,696
(E) can not be determined
Rationale: Let the side for growing cabbages this year be X ft. Thus the area is X^2.
Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.
The area would have increased by 197 sq ft as each cabbage takes 1 sq ft space.
X^2 - Y^2 = 197
(X + Y)(X - Y) = 197
197 is a prime number and thus it will be (99+98)*(99-98).
Thus X = 99 and Y = 98
X^2 = 99^2 = 9801
The answer is A.
Answer: (A) 9801
Question: A man has Rs. 440 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) 45
(B) 82.5
(C) 75
(D) 90
(E) 105
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 440
16x = 440
x = 27.5.
Hence, total number of notes = 3x = 82.5.
Answer = B
Answer: (B) 82.5
Question: Seven people went to a restaurant for dinner. Six of them spent $9 each on their meals and the seventh person spent $12 more than the average expenditure of all seven people. What was the total amount of money that the seven people spent?
(A) $71
(B) $73
(C) $75
(D) $77
(E) $79
Rationale: Let T be the total amount of money spent.
6*9 + (T/7 + 12) = T
66 = 6T/7
T = (7*66)/6 = 77
The answer is D.
Answer: (D) $77
Question: A printer numbers the pages of a book starting with 1 and uses 3189 digits in all. How many pages does the book have ?
(A) 1000
(B) 1074
(C) 1075
(D) 1080
(E) 1090
Rationale: No.of digits in 1-digit page nos=1*9=9
" " 2-digit " =2*90=180
3-digit " =3*900=2700
" " 4-digit " =3189-(9+180+2700)=300
therefore no.of 4-digit page no's=300/4=75
total no.of pages=999+75=1074
ANSWER:B
Answer: (B) 1074
Question: If x = 1- 5t and y = 2t - 1, then for what value of t does x = y?
(A)  5/2
(B)  3/2
(C)  2/3
(D)  2/7
(E)  0
Rationale: We are given x = 1 – 5t and y = 2t – 1, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 5t for x and 2t – 1 for y in the equation x = y. This gives us:
1 – 5t = 2t – 1
2 = 7t
2/7 = t
The answer is D.
Answer: (D)  2/7
Question: In the biology lab of "Jefferson" High School there are 4.32*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?
(A) 100
(B) 200
(C) 400
(D) 1000
(E) 5000
Rationale: 4.32*10^6/ 10800==> 43.2*10^3/108==> 43200/108= 400
ANSWER:C
Answer: (C) 400
Question: A train 300 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) 298 m
(B) 268 m
(C) 500 m
(D) 267 m
(E) 1000 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, (300 + x)/60 = 65/3
x = 1000 m.
Answer: E
Answer: (E) 1000 m
Question: A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1100. How many workers were part of the latter production run?
(A) 26
(B) B)10
(C) C)11
(D) D)15
(E) E)23.5
Rationale: The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1
5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 1100 .. thus for the current period = 1100 -500 = 600
(5n+45)K= 600
k = 600/5n+45........................................2
equate 1 and 2
500/5n+20 = 600 /5n+45
500(5n+45) = 600(5n+20)
2500n + 22500 = 3000n + 12000
-500n = -10500
n = 21
thus n+5 = 26
hence A
Answer: (A) 26
Question: A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: 1 Yard = 36 inches
Total length of ribbon = 4 yards = 4*36 inches = 144
Length of ribbon needed for 1 bow = 15 inches
Max number of bows that can be made = 144 / 15
= 9.6
Answer B
Answer: (B) 9
Question: If BURNER is coded as CASOIS then how will ALIMENT be coded?
(A) BKJLFMU
(B) EKOLIMS
(C) EMONIOU
(D) BRJSFTU
(E) EROSITU
Rationale: You take the next consonant or vowel in alphabetical sequence.
Watch:
b - c (next consonant in sequence)
u - a (aeiou, u cycles back to beginning, or a)
r - s
n = o
e = i (next vowel)
r = s
therefore:
a = e (next vowel)
l = m
i = o
m = n
e = i
n = o
t = u
EMONIOU
ANSWER:B
Answer: (B) EKOLIMS
Question: The total of a company's assets in 1994 was 50% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
(A) 5.5N
(B) 7.5N
(C) 9.5N
(D) 11.5N
(E) 13.5N
Rationale: In 1992, the company's assets were N.
In 1993, the company's assets were N + 4N = 5N.
In 1994, the company's assets were 5N + 2.5N = 7.5N.
The answer is B.
Answer: (B) 7.5N
Question: If the set S is composed of the following numbers {99, 100, 100, 105, 106, 112, 127}, which of the following is largest?
(A) The average (arithmetic mean) of set S
(B) The median of set S
(C) The mode of set S
(D) The range of set S
(E) The standard deviation of set S
Rationale: A) 99, 100, 100, 105, 106, 112, 127 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 127 -99 = 28.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n =>< 100
IMO option A is correct answer..
Answer: (A) The average (arithmetic mean) of set S
Question: What is the dividend. divisor 13, the quotient is 17 and the remainder is 1
(A) 222
(B) 224
(C) 226
(D) 228
(E) 230
Rationale: A = d * Q + R
A = 13 * 17 + 1
A = 221 + 1
A = 222
Answer: (A) 222
Question: if the price of a book is first decreased by 15% and then increased by 10%, then the net change in the price will be :
(A) 10
(B) 388
(C) 6.5
(D) 29
(E) 22
Rationale: Explanation:
Let the original price be Rs. 100.
Decreased by 15% = 85
Then increased 10% on Rs 85 = 85 + 8.5 = 93.5
Net change in price = 100 - 93.5 = 6.5
Answer : C
Answer: (C) 6.5
Question: A truck covers a distance of 360 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?
(A) 6 hours
(B) 5 hours
(C) 7 hours
(D) 8 hours
(E) None
Rationale: Explanation :
Speed of the truck = Distance/time = 360/8 = 45 kmph
Now, speed of car = (speed of truck + 18) kmph = (45 + 18) = 63 kmph
Distance travelled by car = 360 + 81 = 441 km
Time taken by car = Distance/Speed = 441/63 = 8 hours.
Answer – D
Answer: (D) 8 hours
Question: A car crosses a 600m long bridge in 5 mins. What is the speed of car in km per hr?
(A) 7 km/hr
(B) 7.2 km/hr
(C) 7.5 km/hr
(D) 8 km/hr
(E) 8.5 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: (B) 7.2 km/hr
Question: A can contains a mixture of liquids A and B is the ratio 7:5. When 12 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many liter of liquid A was contained by the can initially?
(A) 25
(B) 27
(C) 29
(D) 28
(E) 31
Rationale: Ci*Vi = Cf*Vf
(7/12)*(V1 - 12) = (7/16)*V1
(V1 - 12)/V1 = 3/4
12 accounts for the difference of 1 on ratio scale so Initial volume = V1 = 4*12 = 48 litres.
7/12 of the initial mixture was liquid A so liquid A was (7/12)*48 = 28 litres.
Answer : D
Answer: (D) 28
Question: 10% of the inhabitants of village having died of cholera.,a panic set in , during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
(A) 600
(B) 6500
(C) 6000
(D) 6500
(E) 7000
Rationale: Let the total number of orginal inhabitants be x.
((75/100))*(90/100)*x)=4050  (27/40)*x=4050
x=((4050*40)/27)=6000.
ANSWER C 6000
Answer: (C) 6000
Question: John found that the average of 15 numbers is 40. If 12 is added to each number then the mean of number is?
(A) 52
(B) 45
(C) 65
(D) 78
(E) 64
Rationale: (x+x1+...x14)/15 = 40
52
Option A
Answer: (A) 52
Question: Two numbers are respectively 20% and 60% more than a third number. The percentage that is first of the second is?
(A) 34%
(B) 68%
(C) 51%
(D) 75%
(E) 83%
Rationale: I II III
120 160 100
160----------120
100-----------? => 75%
Answer:D
Answer: (D) 75%
Question: If a train runs at 40 kmph ,it reach its destination late by 11 minutes but if it runs at 50kmph it is late by 5 minutes only . the correct time for a train to complete its journey is?
let the correct time to complete the journey be x min
distance covered in(x+11)min. at 40 kmph
distance covered in(x+5)min. at 50 kmph
(x+11)/60*40=(x+5)/60*50
x=19min
(A) 19 min
(B) 19hrs
(C) 52min
(D) 126min
(E) 52min
Rationale: let the correct time to complete the journey be x min
distance covered in(x+11)min. at 40 kmph
distance covered in(x+5)min. at 50 kmph
(x+11)/60*40=(x+5)/60*50
x=19min
Answer(A)
Answer: (A) 19 min
Question: The traffic lights at 3 different roads change after every 14 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously.
(A) 9:22:12
(B) 9:42:15
(C) 10:15:24
(D) 9:40:12
(E) 10:01:20
Rationale: LCM of 14,72,108 = 1512 = 25mnts 12sec
The lines will change every 25m 12sec
The light will change again after 9:15 AM is = 9:15+0:25:12 = 9:40:12
Answer is D
Answer: (D) 9:40:12
Question: How many positive 5-digit integers have the odd sum Q of their digits?
(A) 9*10^2
(B) 9*10^3
(C) 10^4
(D) 45*10^3
(E) 9*10^4
Rationale: We are looking at numbers between 10000 and 99999 both inclusive.
There are 90000 numbers.
Now for
10000 : sum of digits is odd;
10001 :sum of digits is even;
10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.
(Exception for the above statement :
When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd
and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)
This means exactly half of the numbers will have odd sum Q of their digits. i.e 45000
Answer :D
Answer: (D) 45*10^3
Question: How many inches are in 2000 millimeters? (round your answer to the nearest hundredth of of an inch).
(A) 48.74 inches
(B) 58.74 inches
(C) 78.74 inches
(D) 28.74 inches
(E) 88.74 inches
Rationale: One inch is the same as 25.4 mm. Let x inches be the same as 1000 mm
x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches
correct answer C
Answer: (C) 78.74 inches
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 4?
(A) 123,750
(B) 164,850
(C) 164,749
(D) 149,700
(E) 156,720
Rationale: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 4
Seeing the Options After Dividing and Finding the Reminder of 2
My Answer was A
Answer: (A) 123,750
Question: A bag contains 3 white balls, 3 black balls & 2 red balls. One by one three balls are drawn out without replacement. What is the probability that the third ball is red?
(A) 0.25
(B) 0.15
(C) 0.35
(D) 0.45
(E) 0.4
Rationale: Favorable outcomes :
WWR -> P(WWR)= 3/8 * 2/7 * 2/6 = 12/336
WRR -> P(WRR)= 3/8 * 2/7 * 1/6 = 6/336
RWR -> P(RWR)= 2/8 * 3/7 * 1/6 = 6/336
BBR -> P(BBR)= 3/8 * 2/7 * 2/6 = 12/336
BRR -> P(BRR)= 3/8 * 2/7 * 1/7 = 6/336
RBR -> P(RBR)= 2/8 * 3/7 * 1/6 = 6/336
WBR -> P(WBR)= 3/8 * 3/7 * 2/6 = 18/336
BWR -> P(BWR)= 3/8 * 3/7 * 2/6 = 18/336
So, P(Total) = 84/336 = 1/4 = 0.25
Answer is A
Answer: (A) 0.25
Question: If x is an integer such that 0 < x < 12, 1 < x < 15, 10 > x > 5, 11 > x > 8, and x + 2 < 12, then x is
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: 0 < x < 12,
1 < x < 15,
-5 < x < 10
8< x < 11
x<10
From above: 8 < x < 10 --> x = 9.
Answer: D.
Answer: (D) 9