RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Given that a “24-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 8-inch pizza to a 24-inch pizza gives you approximately what percent increase in the total amount of pizza?
A.330
B.500
C.670
D.800
Answer: D.800
Explanation: area of 8 inch pizza= 4*4*pi=16 pi
area of 24 inch pizza =12*12*pi=144 pi
128/16*100=800 increase
hence answer is D
Question: If c ≠ 1 and if dc/(d - c) = 1, what is the value of d in terms of c?
A.(c-1)/c
B.c/(1-c)
C.c/(c + 1)
D.(c + 1)/c
Answer: B.c/(1-c)
Explanation: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
B
Question: P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?
A.60/11
B.61/11
C.71/11
D.72/11
Answer: A.60/11
Explanation: Explanation:
P can complete the work in (12 * 8) hrs = 96 hrs
Q can complete the work in (8 * 10) hrs=80 hrs
P's 1 hour work=1/96 and Q's 1 hour work= 1/80
(P+Q)'s 1 hour's work =(1/96 + 1/80)=11/480
so both P and Q will finish the work in 480/11hrs
Number of days of 8 hours each =(480/11 * 1/8)=60/11
ANSWER IS A
Question: Find the number of different 4-letter words with or without meaning that can be formed from the letters of the word " NUMBER"
A.340
B.360
C.320
D.420
Answer: B.360
Explanation: There are 6 letters in the word "NUMBER". So the number of 4-letter words 6P4 =360 Answer : B
Question: How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated?
A.20
B.16
C.8
D.24
Answer: A.20
Explanation: Explanation :
A number is divisible by 5 if the its last digit is a 0 or 5
We need to find out how many 3 digit numbers can be formed from the 6 digits (2,3,5,6,7,9)
which are divisible by 5.
Since the 3 digit number should be divisible by 5, we should take the digit 5
from the 6 digits(2,3,5,6,7,9) and fix it at the unit place.
There is only 1 way of doing this
1
Since the number 5 is placed at unit place, we have now five digits(2,3,6,7,9) remaining.
Any of these 5 digits can be placed at tens place
5 1
Since the digits 5 is placed at unit place and another one digits is placed at tens place,
we have now four digits remaining. Any of these 4 digits can be placed at hundreds place.
4 5 1
Required Number of three digit numbers = 4 x 5 x 1 = 20.. Answer : Option A
Question: In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 8 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?
A.15
B.25
C.30
D.45
Answer: C.30
Explanation: This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...
We're told that the ratio of the number of dogs to the number of cats is 15:7. We're then told that 8 more cats are added to this group and the ratio becomes 15:11. We're asked for the number of dogs.
Algebraically, since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7, we can write this initial relationship as...
15X/7X
When we add the 18 cats and factor in the 'ending ratio', we have an equation....
15X/(7X+8) = 15/11
Here we have 1 variable and 1 equation, so we can solve for X....
(15X)(11) = (7X+8)(15)
(X)(11) = (7X+8)(1)
11X = 7X + 8
4X = 8
X = 2
With this X, we can figure out the initial number of dogs and cats...
Initial dogs = 15X = 15(2) = 30
Final Answer: C
Question: Before being simplified, the instructions for computing income tax in country R were to add 7 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?
A.50 + I/200
B.50 + 15I/100
C.50+ I/40
D.100+ I/50
Answer: B.50 + 15I/100
Explanation: Income of a person is I
7 percent of ones annual income = 7I/100
100 units of Country R's currency = 100
1 percent of one's annual income = I/100
Average of 100 units and 1 percent annual income = 50 + I/200
Sum of average and 7 percent = 7I/100 + 50 + I/200
= 50 + 15I/200
So answer is B.
Question: A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?
A.Rs. 9228
B.Rs. 9129
C.Rs. 9120
D.Rs. 9000
Answer: D.Rs. 9000
Explanation: Let B's capital be Rs. x.
{3500\12}/{7x}={2}/{3}
=> x = 9000.
Answer: D
Question: Darcy lives 1.5 miles from work. She can walk to work at a constant rate of 3 miles per hour, or she can ride the train to work at a constant rate of 20 miles per hour. If she rides the train, there is an additional x minutes spent walking to the nearest train station, waiting for the train, and walking from the final train station to her work. If it takes Darcy a total of 5 more minutes to commute to work by walking than it takes her to commute to work by riding the train, what is the value of x?
A.20.5
B.15
C.25.5
D.30
Answer: A.20.5
Explanation: The time it takes Darcy to walk to work is (1.5/3)*60 = 30 minutes
The time it takes Darcy to take the train is (1.5/20)*60 + x = 4.5 + x minutes
It takes 15 minutes longer to walk, so 30 = 4.5 + x + 5
x=20.5 minutes
Answer: A
Question: 36^6 is equal to which of the following?
A.2,176,782,336
B.2,176,782,330
C.2,176,782,334
D.2,176,782,338
Answer: A.2,176,782,336
Explanation: A is the correct answer. We do not really need to calculate it. The last digit for 36^6 will be 6. Hence A is the correct answer
Question: Seven points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
A.4
B.5
C.6
D.0
Answer: D.0
Explanation: Number of triangles can be formed out of 6 points= 7C3=35
Number of quadrilaterals can be formed out of 6 points= 7C4=35
35-35=0.
Answer=D
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.27000 after completion of one year. What will be Jose's share of profit?
A.20000
B.15000
C.25000
D.34000
Answer: B.15000
Explanation: SoL = ~s- So Anju’s share = [5/9] x 27000 = 15000
B
Question: If 3x+4y=60 and 6x-4y=12, what is the product of x and y?
A.80
B.54
C.54
D.72
Answer: D.72
Explanation: Given 3x+4y=60 ---Eq 1
6x -4y =12 -- Eq 2
Sum both eqns we get 9X = 72 => X = 8
sum 6X in eq 2 => 48 - 4y = 12.
=> Y = 9
Now XY = 8 * 9 = 72
Option D is correct answer.
Question: If the sum of a number and its square is 272, What is the number?
A.14
B.16
C.19
D.21
Answer: B.16
Explanation: Explanation:
Let the integer be x.
Then, x + x2 = 272
x2 + x - 272 = 0
(x + 17) (x – 16) = 0
x = 16
ANSWER: B
Question: Find the smallest number which should be multiplied with 36963 to make it a perfect square.
A.4
B.7
C.4
D.3
Answer: D.3
Explanation: 36963 = 111*111*3
Required smallest number = 3
3 is the smallest number which should be multiplied with 36963 to make it a perfect square.
ANSWER:D
Question: When 18 is divided by the positive integer k, the remainder is 4, for how many different values of k is this true?
A.1
B.2
C.4
D.6
Answer: B.2
Explanation: When 18 is divided by k, remainder is 4 i.e. there are 4 balls leftover after grouping. so k must be greater than 4.
It also means that 14 is completely divisible by k.
Factors of 14 are 1, 2, 7, 14.
Out of these, k can be 7 and 14.
Answer (B)
Question: A contractor undertakes to built a walls in 50 days. He employs 40 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
A.60
B.30
C.35
D.20
Answer: A.60
Explanation: 40 men complete 0.4 work in 25 days.
Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1
we have,
40 × 25 × 0.6 = m2 × 25 × 0.4
or m2 = 40×25×0.6/25×0.4 = 60 men
AnswerA
Question: There are 2 more women than there are men on a local co-ed softball team. If there are a total of 16 players on the team, what is the ratio of men to women?
A.10/16
B.7/9
C.4/16
D.6/10
Answer: B.7/9
Explanation: w = m+2
w+m = 16
m+2+m = 16
2m = 14
m = 7
w = 9
ratio:7:9
Ans: B
Question: For which of the following functions is f(z) = f(−z) for all values of z ?
A.f(x) = x^3 + 3
B.f(x) = −x
C.f(x) = 2x + 3
D.f(z) = −z^2 + 2
Answer: D.f(z) = −z^2 + 2
Explanation: f(z) = f(−z)
The above is a property of an even function .
f(z) = f^(n)
f(z) = f(−z) will hold when n is an even integer .
The only case when z is even is option D
Answer D
Question: Find 10 / 11 =110 / ?
A.111
B.1100
C.121
D.100
Answer: C.121
Explanation: Answer
Let 10/11 = 110/N,
Then, 10N = 11 x 110
∴ N = (11 x 110) /10 = 121.
Option: C
Question: How many more years will it take to get another Rs.420 compound interest, if Rs.210 doubled in 2 years when compounded annually.?
A.2 years
B.3 years
C.1 years
D.4 years
Answer: A.2 years
Explanation: Explanatory Answer
Rs.210 invested in compound interest becomes Rs.220 in 2 years.
The amount will double again in another 2 years.
i.e., the amount will become Rs.240 in another 5 years.
So, to earn another Rs.220 interest, it will take another 2 years.
Answer A
Question: Amit and Meghna went to New York for a 63 day holiday .Each day ,Amit
spent as many as hundred dollar bills as the remaining number of days in the
trip (excluding the current day ) ,and Meghna spent as many as hundred
dollar bills as the number of days already spent (including current day).
How much per day would they have spent together during the holiday ?
A.$12,600
B.$10000
C.$6300
D.$5000
Answer: C.$6300
Explanation: amith total expense is 100*(62+61......+1) and meghana is 100*(1+2+....63).
tola is 100(62+61....+1+1+2+....63) which can also be written as 100(63)+100*2*(62+61....+1)
expense per day is ((100*63)+(200*(62+61+.....1))/63 which gives 6300 result
ANSWER:C
Question: If the value of a piece of home decreases by 10% while the new tax rate on the home represent 110% of the original tax rate, what is the effect on the taxes?
A.a - taxes increase by 10%
B.b- taxes increase by 1%
C.c- there is no change in taxes
D.d- taxes decrease by 1%
Answer: D.d- taxes decrease by 1%
Explanation: Cansider the value of home = 100, Original tax rate 10%, hence tax value = 100*10% = 10.
Decreased value of home = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9
10-9.9 = decrease by 1%.
Answer D.
Question: The speed of a car is 80 km in the first hour and 60 km in the second hour. What is the average speed of the car?
A.70 kmph
B.92 kmph
C.75 kmph
D.65 kmph
Answer: A.70 kmph
Explanation: S = (80 + 60)/2 = 70 kmph
A
Question: A boat can travel with a speed of 42 km/hr in still water. If the speed of the stream is 10 km/hr, find the time taken by the boat to go 74 km downstream
A.1 hour 40 min
B.2 hour 40 min
C.1 hour 25 min
D.1 hour 30 min
Answer: C.1 hour 25 min
Explanation: Speed of the boat in still water = 42 km/hr
speed of the stream = 10 km/hr
Speed downstream = (42+10) = 52 km/hr
Distance travelled downstream = 74 km
Time taken =distance/speed
=74/52
= 1.42 hours
= 1 hour 25 min.
ANSWER:C
Question: Solve for x: 2x â€“ y = (3/4)x + 3.
A.(y + 6)/5
B.4(y + 3)/5
C.(y + 6)
D.4(y - 6)/5
Answer: B.4(y + 3)/5
Explanation: Solution:
2x â€“ y = (3/4)x + 3.
or, 2x - (3/4)x = y + 3.
or, (8x -3x)/4 = y + 3.
or, 5x/4 = y + 3.
or, 5x = 4(y + 3).
or, 5x = 4y + 12.
or, x = (4y + 12)/5.
Therefore, x = 4(y + 3)/5.
correct answer B
Question: How many minutes does it take John to type a words if he types at the rate of b words per minute?
A.b/a
B.a/b
C.ab
D.60a/b
Answer: B.a/b
Explanation: time*rate=job --> time*b=a --> time=a/b.
Answer: B.
Question: Carl can wash all the windows of his house in 6 hours. His wife Maggie can wash all the windows in 5 hours. How many hours will it take for both of them working together to wash all the windows?
A.2
B.2 1/4
C.11 8/2
D.4 1/2
Answer: C.11 8/2
Explanation: Work hrs=AB/(A+B)= 30/11 =11 8/2
Answer is C
Question: An empty pool being filled with water at a constant rate takes 6 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
A.5 hr 30 min
B.5 hr 20 min
C.4 hr 00 min
D.3 hr 12 min
Answer: C.4 hr 00 min
Explanation: (3/5) of a pool/ 6 hours = 3/30 = 1/10 (the rate)
(1 pools/10 hours) = (2/5* pool)/ x hours
Cross multiply x = (2/5) 10
x = 4
C
Question: Look at this series: 664, 332, 340, 170, ____, 89, ... What number should fill the blank?
A.100
B.126
C.172
D.178
Answer: D.178
Explanation: D
178
This is an alternating division and addition series: First, divide by 2, and then add 8.
Question: The average age of a class of 23 students is 22 years. The average increased by 1 when the teacher's age also included. What is the age of the teacher?
A.40
B.41
C.46
D.42
Answer: C.46
Explanation: Total age of all students =23Ã—22
Total age of all students + Age of the teacher =24Ã—23
Age of the teacher
=24Ã—23âˆ’23Ã—22=23(24âˆ’22)=23Ã—2=46
Answer is C.
Question: A train passes a station platform in 36 sec and a man standing on the platform in 22 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.767 m
B.210 m
C.187 m
D.176 m
Answer: B.210 m
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 22 = 330 m.
Let the length of the platform be x m . Then,
(x + 330)/36 = 15 => x = 210 m.
Answer:B
Question: Rates for having a manuscript typed at a certain typing service are $6 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
A.$690
B.$620
C.$650
D.$640
Answer: A.$690
Explanation: For 100-30-10=60 pages only cost is 6$ per page for the first time page is typed - 60*5=300$;
For 30 pages the cost is: first time 6$ + 3$ of the first revision - 30*(6+3)=270$;
For 10 pages the cost is: first time 5$ + 3$ of the first revision + 3$ of the second revision - 10(6+3+3)=120$;
Total: 300+270+120=690$.
Answer: A.
Question: Rahim bought 55 books for Rs.1500 from one shop and 60 books for Rs.340 from another. What is the average price he paid per book ?
A.s.17
B.s.18
C.s.16
D.s.11
Answer: C.s.16
Explanation: Average price per book
= (1500+ 340) / (55+ 60) = 1840/ 115
= Rs.16
Answer:C
Question: 1, 1, 3, 9, 5, 25, 7, 49 _, 81
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: as seq is
1, 1, 3, 9, 5, 25, 7, 49 9, 81
two series are there.
1,3,5,7,9 ...odd numbers
and 1,9,25,49,81 .. square of odd numbers
ANSWER:D
Question: A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
A.17%
B.25%
C.69%
D.31%
Answer: A.17%
Explanation: Let the price be 100.
The price becomes 130 after a 30% markup.
Now a discount of 10% on 130.
Profit=117-100
17%
answer A
Question: How many integers between 10 and 100 are there such that their unit digit is odd?
A.45
B.50
C.30
D.60
Answer: A.45
Explanation: 90 numbers between - 10 and 100
Out of which half would be even, half odd.
Number of odd unit digit number = 45.
correct option is A
Question: If a,b ,and c are positive real numbers such that a(b+c) = 152, b(c+a) =162 , and c(a+b) = 170, then abc is
A.a) 672
B.b) 688
C.c) 704
D.d) 720
Answer: D.d) 720
Explanation: ab+bc = 152 --------------------------------------1)
bc+ba = 162---------------------------------------2)
ac+ab = 170---------------------------------------3)
Re-writing equation 3 as follows:
ac+cb = 162 + 8
ac+cb = bc+ba + 8
ac = ba + 8 ............... (4)
Adding (1)(4)
2ac = 160
ac= 80
abc has to be multiple of 80, only 720 fits in
Answer = D
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
A.92 sec
B.70 sec
C.90 sec
D.89 sec
Answer: C.90 sec
Explanation: C
90 sec
Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5) = 90 sec.
Question: During a sale of 30% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies. The store still makes a profit of 12% on this sale. What is the mark up percentage on each candy?
A. 100%
B. 80%
C. 75%
D. 66+2/3%
Answer: B. 80%
Explanation: Hi Akhil, I can share the way I solved it..
Let's say Marked price = M
So, there's a discount of 20% on M So, new S.P. = 80% of M
Now, the child convinces the owner to sell 20 candies for the price of 14 candies .
Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of 6/20 *100 = 30%
So, the latest S.P. = 70% of 80% of M = 0.7* 0.8 M
Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,
0.7 * 0.8 * M = 1.12 C.P
So, we get, M= 2 C.P.
i.e. Marked price was kept 100% above C.P.
B
Question: Average of six numbers is 30, and the sum of three of the numbers is 99, wat is the average of the other 3 numbers?
A.27
B.34
C.29
D.35
Answer: A.27
Explanation: Let the six numbers be a, b, c, d, e,f. Then their average is (a+b+c+d+e+f)/6=30a+b+c=99(99+d+e+f)/6=3099+d+e+f=180d+e+f=81average=81/3=27Ans A
Question: For integers a, b, and c, if ab = bc, then which of the following must also be true?
A.A=C
B.A^2*b=b*c^2
C.A/c=1
D.ABC>bc
Answer: B.A^2*b=b*c^2
Explanation: ab=bc
ab=bc --> ab−bc=0.
A. If b−bc=0 then b(a−c)=0 and b(a−c)=0 then b=0 or a=ca.
B. If a^2*b=b*c^2 then b(a2−c2)=b(a2−c2)=0= b(a−c)(a+c)=0
C. If b(a−c)(a+c)=0. Now, since b=0b=0or a=c=a=c,then b(a−c). If (a+c)=b(a−c)(a+c) does equal to zero. So, we have that this options must be true.
Answer: B.
Question: Ayesha's father was 45 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
A.2 years
B.15 years
C.6 years
D.7 years
Answer: B.15 years
Explanation: Explanation:
Mother's age when Ayesha's brother was born = 34 years.
Father's age when Ayesha's brother was born = (45 + 4) = 49 years.
Required difference = (49 - 34) = 15 years.
Answer: Option B
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.27 sec
B.17 sec
C.48 sec
D.96 sec
Answer: C.48 sec
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:C
Question: Each truck from Dolphin Removal Company can haul 800 pounds of trash at a time.
On Wednesday the company has jobs to remove 2400 pounds of trash from one
site, 3200 from another site, and 4800 from a third site. How many total pounds of
trash will be moved by Jones Company that day? How many trips will it take for the
Jones Company to remove all of the trash?
A.5500 lbs.-2 Trips
B.4500 lbs.-9 Trips
C.2500 lbs.-3 Trips
D.10400 lbs.-13 Trips
Answer: D.10400 lbs.-13 Trips
Explanation: Total trash =2400+3200+4800=10400
No. of trips = 10400/800 = 13
Answer : D
Question: If it takes 6 identical printing presses exactly 4 hours R to print 5,000 newspapers, how long would it take 3 of these presses to print 3,000 newspapers?
A.3 hours, 20 minutes
B.4 hours, 20 minutes
C.4 hours, 48 minutes
D.5 hours, 48 minutes
Answer: C.4 hours, 48 minutes
Explanation: 6 presses - 5,000 newspapers - 4 hours ;
3 presses - 2,500 newspapers - 4 hours ;
3 presses - 3,000 newspapers - 4 hours + 1/5*4 hours = 4 hours, 48 minutes (since 2,500+1/5*2,500=3,000) = R.
Answer: C.
Question: In the given series find the number which is wrong.
215,28,63,126,7,343
A.215
B.28
C.126
D.343
Answer: D.343
Explanation: 215=6*6*6-1
28=3*3*3+1
63=4*4*4-1
126=5*5*5+1
7=2*2*2-1
343 should be 7*7*7+1= 344 but it is 343
ANSWER:D
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 80 inclusive?
A.20
B.45
C.100
D.105
Answer: B.45
Explanation: The multiples of ten from 10 to 80 inclusive would be an evenly spaced set with 8 terms - 10, 20, 30,.......80
So average = (First term + Last Term)/2 = (10 + 80)/2 = 90/2 = 45
Hence, the correct answer is B.
Question: 5, 10, 13, 26, 29, 58, 61, (....)
A.128
B.64
C.122
D.125
Answer: C.122
Explanation: Numbers are alternatively multiplied by 2 and increased by 3
5 Ã— 2 = 10
10 + 3 = 13
13 Ã— 2 = 26
26 + 3 = 29
29 Ã— 2 = 58
58 + 3 = 61
61 Ã— 2 = 122
ANSWER C
Question: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
A.2522
B.1758
C.1578
D.1289
Answer: C.1578
Explanation: A = 1600(21/20)3
= 2522
Answer: C
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. In how much time will the trains cross each other?
A.10 sec
B.11 sec
C.12 sec
D.60/7 sec
Answer: A.10 sec
Explanation: A
Relative speed = (54 + 90)* 5/18 = 8 * 5 = 40 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/40 = 10 sec.
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 13 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
A. 18/79
B. 1/6
C. 1/60
D. 1/50
Answer: C. 1/60
Explanation: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/13 = 15
P = 15/900 = 1/60
Ans:C
Question: 10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: Explanation :
Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
=> 5 men and 10 women can complete the work in 7 days
Answer : Option C
Question: Insert the missing number. 2, 7, 8, 17, 16, 27,
A.42
B.22
C.46
D.62
Answer: B.22
Explanation: Explanation :
There are two series here
2, 8, 16, ... (Increase by 6)
7, 17, 27, ... (Increase by 10)
Hence, next term is 16+6 = 22
Answer : Option B
Question: Find the number of trailing zeros in the product of (1^1)*(5^5)*(10^10)*(15^15) *(20^20)*(25^25)………. *(50^50).
A.150
B.200
C.250
D.245
Answer: C.250
Explanation: Looking at the numbers it looks like
(1x5)^5
(2x5)^10
...
(10x5)^50
1. Determine the limiting factor. Is it 2 or is it 5? We know that all the numbers are multiple of 5 but not of 2. Thus, the limiting factor in this case is 2. Let's drop all the 5. Then, we count factors of 2 of even multiples.
2^10 = 10
4^20 = 20 + 20
6^30 = 30
8^40 = 40 + 40 + 40
10^50 = 50
250
Answer: C