mathewhe/aqua_rat huggingface dataset:
Question: In how many ways can 8 people, A, B, C, D, E, F, G, H be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
(A) 384
(B) 396
(C) 576
(D) 40224
(E) 696
Rationale: Number of total arrangements = 8!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
8! - (4!*2*2) = 40320 - (24*2*2) = 40224
Answer D
Answer: (D) 40224
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 16 2/8% loss
(C) 17 2/3% loss
(D) 16 87/3% loss
(E) 12 2/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: (A) 16 2/3% loss
Question: Find the probability in a group of 10 students sitting in a row , two of them
always sit next to each other
(A) 0.5
(B) 0.4
(C) 0.3
(D) 0.2
(E) 0.1
Rationale: Assume that these 2 students are 1 and then u can sit is 9! and these 2 students can sit by 2 ways then total ways are 9!*2
and the probability is 9!*2/10! = 1/5=0.2
ANSWER:D
Answer: (D) 0.2
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 883
(C) 739
(D) 789
(E) 813
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer:A
Answer: (A) 230
Question: While driving from A-ville to B-town, Harriet drove at a constant speed of 90 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 160 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?
(A) 138
(B) 148
(C) 150
(D) 162
(E) 192
Rationale: 5hr = 300min.
If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.
Now let plug in ans. D or E and verify which one give same distance on each leg.
D. t= 162min
* leg A-B ---> d = 90.192/60 = 17280/60
* leg B-A ----> d = 160*108/60 = 17280/60
so the correct ans. isE
Answer: (E) 192
Question: A library has an average of 510 visitors on sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a sunday is
(A) 250
(B) 276
(C) 280
(D) 285
(E) None
Rationale: Solution
since the month begins with a sunday , so there will be five sundays in the month.
Required Average	= (510x5+240x25 / 30)
= (8550 / 30)
= 285
Answer D
Answer: (D) 285
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:4. The marks obtained by Vijay and Abhishek are in the ratio of?
(A) 3:4
(B) 3:5
(C) 6:5
(D) 3:6
(E) 3:8
Rationale: 4:5
3:4
-------
12:15:20
12:20 ------>6:10
3:5
Answer: B
Answer: (B) 3:5
Question: If a box containing 16 glass frames are dropped, which of the following cannot be the ratio of broken glass frames to unbroken glass frames?
(A) 7 : 2
(B) 1 : 1
(C) 3 : 5
(D) 1 : 7
(E) 1 : 5
Rationale: Explanation :
Solution: For dividing 16 into two whole numbers, the sum of the ratio terms must be a factor of 16.
So, they cannot be in the ratio 7 : 2.
Answer : A
Answer: (A) 7 : 2
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Qâ€™s amount. At the end of the year 35% profit was earned which was equal to 98,000. What was the amount invested by R?
(A) 2,10,000
(B) 1,05,000
(C) 1,75,000
(D) Data inadequate
(E) 60,000
Rationale: Ratio for amount invested by P, Q & R
= 5x Ã— 12 : 6x Ã— 12 : 6x Ã— 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 35% of T
where, T = Total amount
T = 280000
Amount received by
R = 3x /3x+6x+5x(280000)
= 60000
Answer E
Answer: (E) 60,000
Question: A man rides at the rate of 20km/hr. But stops 10minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 175 kilometers?
(A) 9hr
(B) 8 hr 30 min
(C) 9hr 45min
(D) 6hr 20min
(E) 8hr 40min
Rationale: speed of man = 20km/hr
number of rests = (175/25)-1 = 6
time taken for the man = (175/20)+6*(10/60) = 9 hr 45 min
Answer is C
Answer: (C) 9hr 45min
Question: A train 360 metre long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 metre long?
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Speed =45 km/hr=45×5/18=25/2 m/s Distance travelled = (Speed x Time)
Time = (Distance travelled / Speed)
Distance travelled = Length of the train + Length of the platform
=360+140=500 m
= 500/ 25/2 = 40 sec
Answer: C
Answer: (C) 40
Question: Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers?
(A) 21, 12
(B) 9, 0
(C) 15, 6
(D) 10, 1
(E) 14, 5
Rationale: the larger number: x
the smaller number: y
twice the larger: 2x
three more than five times the smaller: 5y + 3
relationship between ("is"): 2x = 5y + 3
four times the larger: 4x
three times the smaller: 3y
relationship between ("sum of"): 4x + 3y = 71
Now I have two equations in two variables:
2x = 5y + 3
4x + 3y = 71
I will solve, say, the first equation for x:
x = (5/2)y + (3/2)
Then I'll plug the right-hand side of this into the second equation in place of the "x":
4[ (5/2)y + (3/2) ] + 3y = 71
10y + 6 + 3y = 71
13y + 6 = 71
13y = 65
y = 65/13 = 5
Now that I have the value for y, I can solve for x:
x = (5/2)y + (3/2)
x = (5/2)(5) + (3/2)
x = (25/2) + (3/2)
x = 28/2 = 14
Answer: E
Answer: (E) 14, 5
Question: If 24 men take 15 days to to complete a job, in how many days can 18 men finish that work?
(A) 20
(B) 19
(C) 18
(D) 17
(E) 16
Rationale: Ans. 20 days
Answer: (A) 20
Question: Whats the reminder when 445,876,985,420,215,546,656,452 is divided by 8
(A) 1
(B) 7.
(C) 4
(D) 3
(E) 9
Rationale: A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8.
Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.
445,876,985,420,215,546,656,452 =445,876,985,420,215,546,656,000+452
The first number is divisible by 8. You just have to find the remainder when you divide 452 by 8. That will be the remainder when you divide the original number by 8.
452/8 gives remainder 4.
Answer (C)
Answer: (C) 4
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4
(B) 4/3
(C) 4/5
(D) 4/9
(E) 4/7
Rationale: Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8/14 = 4/7
Hence Answer is E
Answer: (E) 4/7
Question: Each signal that a certain ship can make is comprised of 3 different flags hanging vertically in a particular order. How many unique signals can be made by using 4 different flags?
(A) 10
(B) 12
(C) 20
(D) 24
(E) 36
Rationale: Consider a flagpole with 3 vertical slots for flags
As we have to select different flags we can do as follows
topmost flag can be paced in 4 ways
middle flag can be placed in 3 ways
bottom most flag can be placed in 2 ways
(order doesn't matter the selection matters)
Total ways = 4 * 3 * 2 = 24 ways
correct answer - D
Answer: (D) 24
Question: A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C to D?
(A) 7
(B) 4
(C) 6
(D) 3
(E) 2
Rationale: Since B and D are twins, so B = D.
Now, A = B + 3 and A = C - 3.
Thus, B + 3 = C - 3 D + 3 = C-3 C - D = 6.
Answer: C
Answer: (C) 6
Question: The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together?
(A) 40
(B) 98
(C) 27
(D) 29
(E) 22
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 60 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2
= (60 + 20) / 2
= 40.
Answer:A
Answer: (A) 40
Question: In 1995 a certain store had 1,800 tools in stock that had been purchased for $20 each. If 1,000 of these tools were sold in 1995 for $40 each and the remaining 800 were sold in 1996 for $50 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?
(A) $0
(B) $6,000
(C) $8,000
(D) $32,000
(E) $40,000
Rationale: The keyword here isGross Profit:
Gross Profit = (Selling Price - Original Price)*(# of Items Sold)
So lets figure out what the Gross Profit for 1995:
GP1995 = (40-20)*(1000) = 20000
And the Gross Profit for 1996:
GP1996 = (50-20)*(800) = 24000
So the difference would be:
24000-20000 = 4000
ANSWER: B. 4000
Answer: (B) $6,000
Question: Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 15 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.
After 40 minutes Annie is 2 km ahead.
In the next 15 minutes, Sam rides 3 km so Sam will be 1 km ahead.
It will take Annie 20 minutes to catch Sam.
The answer is A.
Answer: (A) 20
Question: Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is?
(A) 17 years
(B) 97 years
(C) 38 years
(D) 18 years
(E) 19 years
Rationale: Let Rajan's present age be x years.
Then, his age at the time of marriage = (x - 8) years.
x = 6/5 (x - 8)
5x = 6x - 48 => x = 48
Rajan's sister's age at the time of his marriage = (x - 8) - 10 = 30 years.
Rajan's sister's present age = (30 + 8) = 38 years.
Answer: C
Answer: (C) 38 years
Question: In My, Xiang sold 15 used cars. For these 15 used cars the range of selling prices was 12,000 and the lowest selling price was 4,500. In June, Xiang sold 10 cars. For these 10 cars the range of selling was 16,000 and the lowest selling price was 6,100. What was the range of selling prices for the 25 used car sold by xiang in May and June?
(A) 15,600
(B) 15,750
(C) 16,820
(D) 18,100
(E) 19,200
Rationale: for 10 cars - 16000+ 6100 = 22,100
for 15 cars - 12000+ 4500 = 19,500
max = 22,100 min 4500
answer is approx 17600.
Option D is closest.
Answer: (D) 18,100
Question: Find out the wrong term in the series 1, 2, 2, 4, 8, 12
(A) 12
(B) 24
(C) 32
(D) 16
(E) 36
Rationale: Explanation:
Each number with in the series is the product of the two numbers that proceed it.
So, if (2 * 2 = 4) , then (4 * 8= 32 ). 32 should replace 12.
Answer: C) 32
Answer: (C) 32
Question: A and B can do a piece of work in 4 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in?
(A) 4 DAYS
(B) 21 DAYS
(C) 13 DAYS
(D) 12 DAYS
(E) 3 DAYS
Rationale: C = 1/3 – 1/4 = 1/12 => 12 days
Answer:D
Answer: (D) 12 DAYS
Question: A baseball card decreased in value 25% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 28%
(B) 30%
(C) 32.5%
(D) 36%
(E) 72%
Rationale: Let the initial value of baseball card = 100
After first year , value of baseball card = (1- 25/100)* 100 = 75
After second year , value of baseball card =(1 - 10/100)* 75 = 67.5
total percent decrease of the card's value over the two years = (100-67.5)/100 *100%
=31.5%
Answer C
Answer: (C) 32.5%
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $160, how much more remains to be paid?
(A) $880
(B) $990
(C) $1,000
(D) $1,100
(E) $1,440
Rationale: 10/100P = 160 >> p= 160*100/10 = 1600
1600 - 160 = 1440
ANSWER:E
Answer: (E) $1,440
Question: Find the odd man out. 445, 221, 109, 46, 25, 11, 4
(A) 25
(B) 109
(C) 46
(D) 221
(E) 11
Rationale: Explanation :
To obtain next number, subtract 3 from the previous number and divide the result by 2
445
(445-3)/2 = 221
(221-3)/2 = 109
(109-3)/2 = 53
(53-3)/2 = 25
(25-3)/2 = 11
(11-3)/2 = 4
Clearly, 53 should have come in place of 46
Answer : Option C
Answer: (C) 46
Question: If 36 men can do a piece of work in 15 hours, in how many hours will 15 men do it?
(A) 22
(B) 36
(C) 60
(D) 88
(E) 72
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 15:36 ::15:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 15) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 15}{15}=36
Hence, 15 men can do it in 36 hours.
Answer: B) 36
Answer: (B) 36
Question: A three digit number divisible by 7 becomes divisible by 3 when 7 is added to it. The largest such number is :
(A) 891
(B) 896
(C) 882
(D) 867
(E) 864
Rationale: Out of all the 5 options, only 896 is NOT divisible by 3. All others are divisible
So Answer = B(No further calculation required)
Addition of any two non-divisible numbers by 3 gives the resultant divisible by 3
7 is non-divisible by 3; we are adding a number to that so that the resultant becomes divisible by 3
Applying the above rule,It means that the number which we are going to add should be non-divisible by 3
So comes the answer = 896
Answer : B
Answer: (B) 896
Question: The area of playground is 5400 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.
(A) a) $144
(B) b) $150.50
(C) c) $151.2
(D) d) $158.60
(E) e) $160.70
Rationale: total volume * unit cost = total cost
or, 5400 * 0.01 * 2.8 = total cost = 151.2=C
Answer: (C) c) $151.2
Question: A single discount equivalent to the discount series of 20%, 10% and 15% is?
(A) 31.9
(B) 31.7
(C) 31.6
(D) 38.8
(E) 31.1
Rationale: 100*(80/100)*(90/100)*(85/100) = 61.2
100 - 61.2 = 38.8
Answer:D
Answer: (D) 38.8
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
(A) 9 : 55
(B) 9 : 29
(C) 9 : 25
(D) 9 : 20
(E) 9 : 27
Rationale: Explanation:
a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22 = 9 : 25
Answer: Option C
Answer: (C) 9 : 25
Question: A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $5.0. If the company’s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?
(A) $960
(B) $1,500
(C) $1,725
(D) $2,050
(E) $2,250
Rationale: Total Volume is 288000
Given LBH = 8*10*12.
the number of hats inside it = 288000/10 * 8 * 12 = 300.
price of each hat is 5 $ then total value is 300 * 5.0 = 1500.
IMO option B is correct answer..
Answer: (B) $1,500
Question: Statement: "In order to bring punctuality in our office, we must provide conveyance allowance to our employees." Assumptions: 1)Conveyance allowance will not help in bringing punctuality. 2)Discipline and reward should always go hand in hand.
(A) Only assumption I is implicit
(B) Only assumption II is implicit
(C) Either I or II is implicit
(D) Neither I nor II is implicit
(E) Both I and II are implicit
Rationale: Assumption I goes against the statement. So, it is not implicit. The allowance will serve as a reward to the employees and shall provoke them to come on time. So, II is implicit.
B)
Answer: (B) Only assumption II is implicit
Question: The ratio between m and y is 7/9; m and y are increased by 4, what is the ratio between the new values of m and y?
(A) 7/9
(B) 14/9
(C) 7/18
(D) 11/13
(E) It Cannot Be Determined
Rationale: Ratio = 7k/9k = 7/9, 14/18, etc.
m and y are increased by 4 --> (7k + 4)/(9k + 4)
New ratio can be 11/13, 18/22, etc.
Answer: E
Answer: (E) It Cannot Be Determined
Question: Find the perimeter of a triangle with sides measuring 7 centimeters, 10 centimeters and 15 centimeters.
(A) 10cm
(B) 15cm
(C) 32cm
(D) 35cm
(E) 20cm
Rationale: perimeter of triangle=a+b+c
Perimeter = 7 cm + 10 cm + 15 cm = 32 cm
Answer: C.
Answer: (C) 32cm
Question: A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/h. The other one walks at 5.4 km/h. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
(A) 66 km/h
(B) 72 km/h
(C) 78 km/h
(D) 81 km/h
(E) None of these
Rationale: 4.5 km/h = (4.5 × 5⁄18) m/sec = 1.25 m/sec.
& 5.4 km/h = (5.4 × 5⁄18) m/sec = 1.5 m/sec.
Let the speed of the train be S m/sec.
Then, (S – 1.25) × 8.4 = (S – 1.5) × 8.5
⇒ 8.4S – 10.5 = 8.5S – 12.75 ⇒ 0.1S = 2.25 ⇒ S = 22.5.
∴ Speed of the train = (22.5 × 18⁄5) km/h = 81 km/h
Answer D
Answer: (D) 81 km/h
Question: The ratio of 2 numbers is 3:4 and their H.C.F. is 4. Their L.C.M. is ?
(A) 32
(B) 48
(C) 60
(D) 52
(E) 12
Rationale: Let the numbers be 3x and 4x
Their H.C.F. = 4
so the numbers are 3*4 , 4*4 = 12,16
L.C.M. = 48
Answer is B
Answer: (B) 48
Question: If c = 9/25, m = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
(A) c, m, w
(B) c, w, m
(C) m, w, c
(D) w, c, m
(E) w, m, c
Rationale: Answer D - w, c, m
c ~ 1/3
m ~ 1/2
and m+w+c = 1 hence w ~ 1/6
Hence increasing order would be w -> c -> m
Answer D
Answer: (D) w, c, m
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1345
(C) 1456
(D) 1567
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 9.
(A) 150
(B) 162
(C) 154
(D) 158
(E) 144
Rationale: D = d * Q + R
D = 17 * 9 + 9
D = 153 + 9
D = 162
ANSWER B
Answer: (B) 162
Question: Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 13 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip?
(A) 48
(B) 42.5
(C) 44
(D) 50
(E) 52.5
Rationale: Total Time taken by jerry = (8/40)*60 Minutes + 13 Minutes + (20/60)*60 Minutes = 35 Minutes
Average Speed = Total Distance / Total Time = (8+20) miles / (35/60)Hours = 28*60 / 35 = 48 Miles per hour
Answer: option A
Answer: (A) 48
Question: The ratio of the volumes of two cubes is 1000 : 1331. What is the ratio of their total surface areas?
(A) 100 : 121
(B) 100 : 127
(C) 81 : 191
(D) 81 : 161
(E) 100 : 182
Rationale: Explanation:
Ratio of the sides = ³√1000 : ³√1331 = 10 : 11
Ratio of surface areas = 10^2 : 11^2 = 100 : 121
Answer: Option A
Answer: (A) 100 : 121
Question: Ramesh and Naresh had a pre-determined number of baskets, at a ratio of 3:1. Ramesh offered 20 of her baskets to Naresh so that the ratio of number of baskets became 8:3. How many more baskets does Ramesh now have than Naresh?
(A) 400
(B) 350
(C) 250
(D) 200
(E) 180
Rationale: Let number of baskets that Ramesh has = R
and number of baskets that Naresh has = N
R/N = 3/1
=>R -3N = 0 --- equation 1
(R-20)/(N+20) = 8/3
=>3R - 60 = 8N+160
=>3R-8N=220 --- equation 2
Multiply equation 1 by 3
3R - 9N = 0
Now , N = 220
R= 660
Number of baskets Ramesh now has more than Naresh = (660-20) - (220+20)
=400
Answer A
Answer: (A) 400
Question: D is the set of all the multiples of 4 between 20 and 100. E is the set of all the factors of 270. Set D and Set E have how many numbers in common?
(A) 3
(B) 1
(C) 0
(D) 5
(E) 12
Rationale: D is a set of multiples of 4.
270 is NOT a multiple of 4, hence none of its factors is a multiple of 4.
Therefore, those two sets won't have any overlap.
Answer: C
Answer: (C) 0
Question: A good train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
(A) 600
(B) 300
(C) 400
(D) 500
(E) 200
Rationale: speed = 78*5/18 m/sec ==>65/3
length of the tunnel be x
then 800+x/60 = 65/3
3(800+x) = 3900
x=500
ANSWER D
Answer: (D) 500
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 12% solution?
(A) A)6.7
(B) B)2.3
(C) C)9.6
(D) D)12.5
(E) E)7.9
Rationale: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=12/100
250+25x=300+3x
22x = 50
x = 2.3
Answer is B
Answer: (B) B)2.3
Question: If 10,364 + x is a multiple of 3, which of the following could be the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: Sum of the digits of 10,364 is 1+0+3+6+4 = 14
Now 14 is not a multiple of 3, the next multiple of 3 close to 14 is 15, which is 1 added to 14.
So the least number to be added to 10,364 is 1
A
Answer: (A) 1
Question: The sum of first seven prime numbers is?
(A) 12
(B) 23
(C) 58
(D) 28
(E) 30
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17) = 58.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
C
Answer: (C) 58
Question: How many times will the digit 3 be written when listing the integers from 1 to 1000?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 3) 3000/10=300 times.
Answer: C.
Answer: (C) 300
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
(A) 47.55 kg
(B) 45.55 kg
(C) 48.55 kg
(D) 49.55 kg
(E) 58.55 kg
Rationale: Required average
= 50.25 x 16 + 45.15 x 8
16 + 8
= 804 + 361.20
24
=	1165.20
24
= 48.55
Answer:C
Answer: (C) 48.55 kg
Question: A train 200 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 17 Kmph
(B) 78 Kmph
(C) 72 Kmph
(D) 36 Kmph
(E) 19 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 200/20
S = 10 M/Sec
Speed= 10*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 36 Kmph
Answer: D
Answer: (D) 36 Kmph
Question: If A = x% of y and B = y% of x, then which of the following is true?
(A) A is smaller than B.
(B) A is greater than B
(C) Relationship between A and B cannot be determined.
(D) If x is smaller than y, then A is greater than B.
(E) None of these
Rationale: Explanation:
x% of y =(x/100 x y )=(y/100 x x )=y% of x
A = B.
ANSWER IS E
Answer: (E) None of these
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 26 years. What is Deepak present age?
(A) 22
(B) 15
(C) 77
(D) 266
(E) 182
Rationale: Present age is 4x and 3x,
=> 4x + 6 = 26 => x = 5
So Deepak age is = 3(5) = 15
Answer: B
Answer: (B) 15
Question: Janexi covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
(A) 1 hour 45 minutes
(B) 2 hours
(C) 2 hours 30 minutes
(D) 3 hours
(E) None of these
Rationale: Janexi covered a distance of 340 miles between city A and city B taking a total of 5 hours. time taken at 60:time taken at 80::(greater speed-average speed):(average speed-lower speed)
average speed is 340/5=68
That gives the answer 3:2=D
Answer: (D) 3 hours