mathewhe/aqua_rat huggingface dataset:
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P+Q+R is:
(A) 16100
(B) 15700
(C) 17500
(D) 16000
(E) 16500
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 x 2) = 10100 .... (i)
Q + R = (6250 x 2) = 12500 .... (ii)
P + R = (5200 x 2) = 10400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv)
(P+Q+R)'s monthly income = Rs. 16500.
Answer:E
Answer: (E) 16500
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
(E) 6
Rationale: 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
Answer: (D) 3
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
(E) 8
Rationale: 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)
Answer: (B) 2
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
(E) None of these
Rationale: 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
Answer: (A) 60
Question: If (A+B) = 4, (B+C) = 8 and (C+D) = 3, what is the value of (A+D)?
(A) 16.
(B) 8.
(C) 7.
(D) 2.
(E) -1.
Rationale: Given A+B = 4
B+C = 8
C+D = 3
Then (A+B)-(B+C)+(C+D)=4-8+3=-1
Option E...
Answer: (E) -1.
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
(E) 4/10
Rationale: w = m+2
w+m = 16
m+2+m = 16
2m = 14
m = 7
w = 9
ratio:7:9
Ans: B
Answer: (B) 7/9
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
(E) f(x) = 5x − 4
Rationale: 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
Answer: (D) f(z) = −z^2 + 2
Question: Find 10 / 11 =110 / ?
(A) 111
(B) 1100
(C) 121
(D) 100
(E) None of these
Rationale: Answer
Let 10/11 = 110/N,
Then, 10N = 11 x 110
∴ N = (11 x 110) /10 = 121.
Option: C
Answer: (C) 121
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
(E) 5 years
Rationale: 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
Answer: (A) 2 years
Question: A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 70 meters apart,then at what speed is the train traveling?
(A) 100km/hr
(B) 110km/hr
(C) 50km/hr
(D) 150km/hr
(E) 210km/hr
Rationale: Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*70 = 3500m = 3.5km
Speed = 60*3.5=210km/hr
Answer is E
Answer: (E) 210km/hr
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
(E) $4000
Rationale: 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
Answer: (C) $6300
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 32 percent alcohol?
(A)  7/2
(B)  5
(C)  20/3
(D)  8
(E)  300/17
Rationale: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 32% of (100+x)
OR
20+x=(100+x)8/25
500+25x=800+8x
17x=300
x=300/17
Ans:E
Answer: (E)  300/17
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%
(E) c- taxes decrease by 10%
Rationale: 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.
Answer: (D) d- taxes decrease by 1%
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
(E) 77 kmph
Rationale: S = (80 + 60)/2 = 70 kmph
A
Answer: (A) 70 kmph
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 5 years and that for 9 years?
(A) 1 : 3
(B) 2 : 3
(C) 1 : 2
(D) 3 : 2
(E) 5 : 9
Rationale: Let the principal be P and rate of interest be R%.
Required ratio =
(P x R x 5)/100 DIVIDED BY	(P x R x 9)/100
=	5PR/9PR	=	5/9	= 5 : 9.
ANSWER : E
Answer: (E) 5 : 9
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
(E) 1 hour 50 min
Rationale: 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
Answer: (C) 1 hour 25 min
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
(E) 5/4(y-6)
Rationale: 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
Answer: (B) 4(y + 3)/5
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
(E) b/(60a)
Rationale: time*rate=job --> time*b=a --> time=a/b.
Answer: B.
Answer: (B) a/b
Question: The sum of three consecutive even numbers is 36, Find the first number?
(A) 21
(B) 18
(C) 12
(D) 16
(E) 10
Rationale: Let the first number be n
Let the second number be n + 2
Let the third number be n + 4
n + n + 2 + n + 4 = 36
Combine like terms:
3n + 6 = 36
3n = 36 - 6
3n = 30
3n = 30
n = 10
n + 2 = 12
n + 4 = 16
The first number is 10
Answer: E
Answer: (E) 10
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
(E) 5
Rationale: Work hrs=AB/(A+B)= 30/11 =11 8/2
Answer is C
Answer: (C) 11 8/2
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
(E) 2 hr 40 min
Rationale: (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
Answer: (C) 4 hr 00 min
Question: Look at this series: 664, 332, 340, 170, ____, 89, ... What number should fill the blank?
(A) 100
(B) 126
(C) 172
(D) 178
(E) 155
Rationale: D
178
This is an alternating division and addition series: First, divide by 2, and then add 8.
Answer: (D) 178
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
(E) 49
Rationale: 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.
Answer: (C) 46
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
(E) 186 m
Rationale: 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
Answer: (B) 210 m
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
(E) $770
Rationale: For 100-30-10=60 pages only cost is 6$ 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.
Answer: (A) $690
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
(E) s.10
Rationale: Average price per book
= (1500+ 340) / (55+ 60) = 1840/ 115
= Rs.16
Answer:C
Answer: (C) s.16
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) 1254
(B) 1376
(C) 1456
(D) 1555
(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: 1, 1, 3, 9, 5, 25, 7, 49 _, 81
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: 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
Answer: (D) 9
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%
(E) 19%
Rationale: 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
Answer: (A) 17%
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
(E) 55
Rationale: 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
Answer: (A) 45
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
(E) e) 750
Rationale: 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
Answer: (D) d) 720
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
(E) 60 sec
Rationale: C
90 sec
Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5) = 90 sec.
Answer: (C) 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%
(E)  55%
Rationale: 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
Answer: (B)  80%
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
(E) 33
Rationale: 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
Answer: (A) 27
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
(E) ba+b+c=0
Rationale: 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.
Answer: (B) A^2*b=b*c^2
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
(E) 6 years
Rationale: 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
Answer: (B) 15 years
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
(E) 17 sec
Rationale: 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
Answer: (C) 48 sec
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
(E) 6500 lbs.-8 Trips
Rationale: Total trash =2400+3200+4800=10400
No. of trips = 10400/800 = 13
Answer : D
Answer: (D) 10400 lbs.-13 Trips
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
(E) 6 hours, 50 minutes
Rationale: 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.
Answer: (C) 4 hours, 48 minutes
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
(E) 625
Rationale: 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
Answer: (D) 343
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
(E) 110
Rationale: 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.
Answer: (B) 45
Question: 5, 10, 13, 26, 29, 58, 61, (....)
(A) 128
(B) 64
(C) 122
(D) 125
(E) 130
Rationale: 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
Answer: (C) 122
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
(E) 2689
Rationale: A = 1600(21/20)3
= 2522
Answer: C
Answer: (C) 1578
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
(E) 90/7 sec
Rationale: A
Relative speed = (54 + 90)* 5/18 = 8 * 5 = 40 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/40 = 10 sec.
Answer: (A) 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
(E)  1/900
Rationale: 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
Answer: (C)  1/60
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
(E) 9
Rationale: 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
Answer: (C) 7
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 15 sec. What is the length of the goods train?
(A) 299
(B) 277
(C) 276
(D) 270
(E) 50
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 15 sec.
Let the length of the train be x meters.
Then, (x + 250)/15 = 20
x = 50 m.
Answer: E
Answer: (E) 50
Question: Insert the missing number. 2, 7, 8, 17, 16, 27,
(A) 42
(B) 22
(C) 46
(D) 62
(E) 68
Rationale: 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
Answer: (B) 22
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
(E) 225
Rationale: 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
Answer: (C) 250
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most
(A) 276
(B) 728
(C) 215
(D) 701
(E) 217
Rationale: Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215.
Answer:C
Answer: (C) 215
Question: 0.6 of a number is equal to 0.08 of another number. The ratio of the numbers will be
(A) 3:4
(B) 4:3
(C) 2:15
(D) 2:9
(E) 3:8
Rationale: Let the numbers be X and Y
0.6X = 0.08Y => X/Y = 0.08/0.6 = 2:15
Answer C.
Answer: (C) 2:15
Question: Which of the following is closer to (5!+4!)/(5!-4!)?
(A) 1
(B) 9
(C) 12
(D) 15
(E) 13
Rationale: Notice that 5! = (5)(4!), so we can factor out 4! from top and bottom.
(5!+4!)/(5!-4!)=[4!(5+1)]/[4!(5-1)]
= 6/4
≈ 1
Answer: A
Answer: (A) 1
Question: It takes John exactly 15 minutes to rake a lawn and it takes his son Todd exactly 30 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn?
(A) 10
(B) 20
(C) 36
(D) 45
(E) 90
Rationale: 1)POE- John takes 15 min so if he takes help of someone else, it has to be less than 30 min..
only A and B are left..
if both do the work in 15 mis each, the combined time will be 7.5 mins
=> 10 A
Answer: (A) 10
Question: X invested $200 in a business and Y invested $300 in a business. At the end of the year they got $1000 as the profit. Find their share?
(A) $100,$200
(B) $200,$300
(C) $300,$400
(D) $400,$500
(E) $400,$600
Rationale: X:Y = 200:300
X:Y = 2:3
X's share = 1000*2/5 = $400
Y's share = 1000*3/5 = $600
Answer is E
Answer: (E) $400,$600
Question: There are two sections X and Y of a class, consisting of 72 and 88 students respectively. If the average weight of sections X is 80 kg and that of sections Y is 70 kg. Find the average weight of the whole class
(A) 70.5
(B) 72.5
(C) 73.5
(D) 74.5
(E) None
Rationale: Solution
Total weight of(72+88)Students	= (72x80+88x70)Kg
= 11920 kg.
Average weight of the whole class	= (11920 / 160)
= 74.50.
Answer D
Answer: (D) 74.5
Question: A man has Rs. 240 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) 60
(C) 75
(D) 90
(E) 105
Rationale: Answer : A
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 240
16x = 240
x = 15.
Hence, total number of notes = 3x = 45.
Answer: (A) 45
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
(A) 60
(B) 100
(C) 120
(D) 180
(E) 200
Rationale: Work done by the waste pipe in 1 min = 1/15-(1/20+1/24)
=-1/40
volume of whole = (3*40)=120 gallons
ANSWER C
Answer: (C) 120