divelab/Sys2Bench huggingface dataset:
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his first child?
Options:
A)12
B)24
C)30
D)48
E)120
Rationale: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and C1 are always together.
Consider F and C1 to be one unit, then we would have total of four units: {FC1}, {M}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and C1 within their unit can be arranged in 2 ways: {FC1} or {C1F}, so total number of arrangements is 4!*2=48.
Answer: D.
Answer: D
Question: If x < y < z and y-x > 1, where x is an even integer and y and z are odd integers, what is the least possible value of z - x?
Options:
A)6
B)3
C)8
D)9
E)10
Rationale: We have:
1) x<y<z
2) y-x>1
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y-x must be odd. since y-x>1, the least value for y-x must be 3, the least value for x must be 2, and, thus, the least possible value for y must be 3 (y-2=1, y=3)
2<3<z, since z is odd, the least possible value for z is 5
z-x=5-2=3
Answer B
Answer: B
Question: A certain city with a population of 144,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
Options:
A)a) 10,700
B)b) 10,800
C)c) 10,900
D)d) 12,000
E)e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 142k
x = 12,000
Answer : D
Answer: D
Question: 2, 6, 12, 20, 30, 42, 56, (...)
Options:
A)62
B)74
C)72
D)81
E)58
Rationale: The pattern is 1×2, 2×3, 3×4, 4×5, 5×6, 6×7, 7×8.
Hence, next number is 8×9 = 72
Answer is C
Answer: C
Question: In what ratio must water be mixed with milk to gain 1623% on selling the mixture at cost price?
Options:
A)6 : 1
B)1 : 6
C)1 : 4
D)4 : 1
E)None of these
Rationale: Explanation :
Let CP of 1 litre milk = Rs.1SP of 1 litre mixture = CP of 1 litre milk = Rs.1Gain=1623%=503%CP of 1 litre
mixture = 100(100+Gain%)×SP=100(100+503)×1=100(3503)=300350=67 By the rule of alligation, we
have
CP of 1 litre water CP of 1 litre milk
0 1
CP of 1 litre mixture
6/7
1 - 6/7 = 1/7 6/7 - 0 = 6/7
Quantity of water : Quantity of milk = 1/7 : 6/7 = 1 : 6
Answer : Option B
Answer: B
Question: Two mixers and one T.V. cost Rs. 7000, while two T.V.s and a mixer cost Rs, 9800. The value of one T.V. is:
Options:
A)Rs.4000
B)Rs.4500
C)Rs.4300
D)Rs.4200
E)None of these
Rationale: Explanation :
Let C.P. of a mixer be Rs. x and that of a T.V. be Rs. y.
Then,
2x + y = 7000 and 2y + x = 9800.
Multiplying 2nd equatien by 2 and subtracting first from it, we get
3y = 19600 - 7000 = 12600
or
y = 4200 C.P. of a T.V. = Rs. 4200
Answer : D
Answer: D
Question: The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p). According to this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 40 percent of the pollutant?
Options:
A) $500,000
B) $100,000
C) $50,000
D) $10,000
E) $5,000
Rationale: To remove 90% of pollutant
C= 100,000(90)/(100-90) = 900,000
To remove 40% of pollutant
C' = 100,000(40)/(100-40) = 400,000
Difference = C - C' = 500,000
Answer - A
Answer: A
Question: The average age of a class of 12 students is 8 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)30 Years
B)31 Years
C)21 Years
D)34 Years
E)49 Years
Rationale: Total age of students is 12X8 = 96 Years
Total age inclusive of teacher = 13X (8+1) = 117
So, Teacher's age is 117-96 = 21 Yrs
There is a shortcut for these type of problems
Teacher's age is 8+(13X1) = 21 Years
C
Answer: C
Question: A man counted his animals, 80 heads and 280 legs (ducks and goats). how many goats are there?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=240 and divide 2d+4g=240 by 2 we get d+2g=140 -----------> eq2
subtract eq1 from eq2
we get no of goats=60
ANSWER:D
Answer: D
Question: A fisherman sells 300 fish for Rs. 9000 at a profit of Rs. 6 per fish. Find his cost price for one metre of cloth?
Options:
A)24
B)36
C)30
D)18
E)20
Rationale: SP per fish = 9000/300 = Rs. 30 Profit per fish = Rs. 6 CP per metre = 30 - 6= Rs. 24Answer: A
Answer: A
Question: Pipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2.5
B)3
C)3.5
D)4
E)4.5
Rationale: The part filled by A + B + C in 1 hour
= 1/6 + 1/8 + 1/24
= 8/24 = 1/3
All the three pipes together will fill the tank in 3 hours.
The answer is B.
Answer: B
Question: If x is the reciprocal of a positive integer, then the maximum value of x^y, where y = –x^2, is achieved when x is the reciprocal of
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Let's take answer C and try to substitute it in the task:
x=13
y=−(13)^2=−1/9
x^y=1/3−1/9
So x will be equal to ninth square root from 33.
And we can infer that maximum value will be when we take x=1 because then x^y will be equal to 1
Answer is A
Answer: A
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 9 and 15 is?
Options:
A)44
B)48
C)46
D)47
E)50
Rationale: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 15 will be divided into 3 parts= 9, 3 and 3 (Making one square and two right triangles)
For the right triangle, height will be= (5^2-3^2)^1/2= 4
And the area of trapezoid = 1/2 (B1+B2)H= 1/2*24*4= 48
B
Answer: B
Question: In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)5.0 sec
B)2.9 sec
C)1.3 sec
D)2.9 sec
E)1.8 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 200/40
= 5.0 sec.
Answer:A
Answer: A
Question: The price of rice falls by 10%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?
Options:
A)5 kg
B)15 kg
C)25 kg
D)30 kg
E)None
Rationale: Solution: Let Rs. 100 be spend on rice initially for 20 kg.
As the price falls by 10%, new price for 20 kg rice,
= (100 -10% of 100) = 90
New price of rice = 90/20 = Rs. 4,5 per kg.
Rice can bought now at = 100/4,5 = 22,22 kg.
Answer: Option E
Answer: E
Question: The total marks obtained by a student in Mathematics and Physics is 40 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
Options:
A)40
B)26
C)27
D)28
E)30
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 40 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (40 + 20) / 2 = 30.Answer:E
Answer: E
Question: Can you find a number such that if we multiply that number by 1 or 2 or 3 or 4 or 5 or 6, then the resultant number contains same all digits (of course in a different place)
Options:
A)143258
B)142876
C)142881
D)142852
E)142857
Rationale: E
142857
Explanation:
142857 * 1 = 142857
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
Note: Such numbers are called cyclic numbers.
Answer: E
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction E of the total distance did he cover while the sun was shining on him?
Options:
A)1/4
B)4/5
C)1/5
D)1/6
E)1/7
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is E=2/14 = 1/7. Answer: E
Answer: E
Question: There are between 90 and 100 cards in a collection of cards. If they are counted out 3 at a time, there is 1 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
Options:
A)91
B)93
C)95
D)97
E)99
Rationale: The numbers with the form 4n+1 are 93 and 97.
Only 97 has the form 3k+1.
The answer is D.
Answer: D
Question: A man can row a boat at 25 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 50 km downstream?
Options:
A)1/2
B)4/3
C)2/3
D)5/3
E)1/3
Rationale: Speed downstream = 25 + 5 = 30 kmph.
Time required to cover 50 km downstream = d/s = 50/30
= 5/3 hours.
Answer: D
Answer: D
Question: The Salary of an employee increase consistently by 15% per year. If his present salary is Rs. 24000 then what will his salary be after 3 years ?
Options:
A)Rs. 32497
B)Rs. 34384
C)Rs. 35065
D)Rs. 36501
E)Rs. 37650
Rationale: Explanation :
Salary = 24000 x 1.15 x 1.15 x 1.15 = 36501
Answer : Option D
Answer: D
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is
Options:
A)1/26
B)1/25
C)1/20
D)1/21
E)1/22
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26.
Answer: A
Answer: A
Question: In how many ways can two members be selected from a group of ten members?
Options:
A)10C2
B)10C8
C)10C4
D)10C3
E)10C1
Rationale: two members can be selected from ten members in
10C6
= 10C2 ways.
Answer: A
Answer: A
Question: In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 7 people read all three newspapers. Find the minimum number of people who read both A and B but not C.
Options:
A)A)1
B)B)2
C)C)3
D)D)0
E)E)5
Rationale: I wish I could draw a diagram to show you but by giving you number A and B, it might help a little.
A and B and C is 7 - that means A and B is at least 7. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C
A and B but not C = |A|-|B| - 7
So i would pick A=35 and B =50 to minimize the value to a 1. (ANS A)
Answer: A
Question: A is 1.5 times as fast as B. A alone can do the work in 30 days. If A and B work on alternative days, beginning with A, in how many days will the work be completed?
Options:
A)23
B)22
C)21
D)36
E)25
Rationale: A can finish 1 work in 30 days
B can finish 1/1.5 work in 30 days - since A is 1.5 faster than B
This means
B can finish 1 work in 30*1.5 days = 45 days
Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 45*30/(45+30) = 20*30/50 = 18 days
Since they alternate on days, it will take them double this time so total time = 18 * 2 = 36 days
So answer is D
Answer: D
Question: An apple orchard grows red and green apples. On the first day of harvest, 496 apples are collected. There are three times as many red apples as there are green apples. How many green apples were harvested?
Options:
A)99
B)112
C)118
D)124
E)130
Rationale: Let x be the number of green apples.
There were 496 total apples; there are three times as many red apples as green apples. Therefore,
x + 3x = 496
4x = 496
x = 124
Answer: D
Answer: D
Question: If A's height is 45% less than that of B, how much percent B's height is more than that of A?
Options:
A)66.66%
B)81.81%
C)66.766%
D)86.66%
E)66.65%
Rationale: Excess of B's height over A's = [(45/(100 - 45)] x 100%
= 81.81%
Answer: B)
Answer: B
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
Options:
A)Rs.500
B)Rs.750
C)Rs.1250
D)Rs.1500
E)Rs.1800
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
ANSWER:D
Answer: D
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $12,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?
Options:
A)62,000
B)85,500
C)95,500
D)100,500
E)100,000
Rationale: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($5,000*2)*2=$20,000 (after 9 years investment will become $5,000*2=$10,000 and in another 9 years it'll become $10,000*2=$20,000).
Answer: A.
Answer: A
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(18 (x – y) (y – z) (z – x))
is equal to :
Options:
A)0
B)1/6
C)1
D)1/4
E)1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(18(x – y) (y – z) (z – x)) = 1/6.
ANSWER:B
Answer: B
Question: If mn > 0, which of the following must be negative?
Options:
A)2m+n
B)2m/n
C)m/n
D)-2mn
E)-m/-n
Rationale: - * + = -
Answer : D
Answer: D
Question: There are 2 sections A and B in a class, consisting of 50 and 40 students respectively. If the average weight of section A is 50kg and that of section B is 70kg, Find the average of the whole class?
Options:
A)50.78kg
B)49.32kg
C)61.67kg
D)58.88kg
E)70.89kg
Rationale: Total weight of 50+40 students = 50*50 + 40*70 = 2500+2800
Average weight of the class is = 5300/90 = 58.88 kg
Answer is D
Answer: D
Question: The median of a triangle is the line from any vertex to the midpoint of the opposite side. Triangle ABC has vertices A = (0, 5), B = (–1, –1), and C = (5, 2). What is the slope of the median from A to the midpoint of BC?
Options:
A)–3/4
B)>–4/3
C)–5
D)–5/2
E)–9/4
Rationale: First to find the midpoint of B & C — average the x-coordinates: (–1+ 5)/2 = 2; and average the y-coordinates: (–1 + 2)/2 = 1/2. Thus, the midpoint has coordinates (2, 1/2). We want the slope from A = (0, 5) to (2, 1/2). The rise is the change in the y-coordinates: 1/2 – 5 = -9/2. The run is the change in the x-coordinates: 2 – 0 = 2. Slope = rise/run = [–9/2]/2 = –9/4. Answer = (E)
Answer: E
Question: A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 3 books from the list, including at most 2 novels. How many selections of 3 books satisfy the requirements?
Options:
A)40
B)115
C)130
D)144
E)195
Rationale: Ans: B
Solution: Selection requires at most 2 novels, means=
0N4P + 1N3P + 2N2P
6c0*4c3+ 6c1*4c2
= 4+ 36
= 40
Ans: A
Answer: A
Question: In a bowl, the number of marbles gets doubled after every minute. If the bowl gets filled after two hours of such process, how long do you think it will take for it to be half filled.
Options:
A)1 hour and 59 minutes
B)2 hour and 59 minutes
C)4 hour and 59 minutes
D)4 hour and 59 minutes
E)5 hour and 59 minutes
Rationale: Solution:
The correct way to solve this question is go backwards. If the number of marble gets doubled every minute and after two hours, it is filled completely, one minute ago it would be half.
So, it will take 1 hour and 59 minutes for it to be filled half.
Answer A
Answer: A
Question: A string of 13 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.02, what is the probability that the string of light bulbs will fail during the time period T?
Options:
A)0.02
B)(0.02)^13
C)1 - (0.02)^13
D)(0.98)^13
E)1 - (0.98)^13
Rationale: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 13 light bulbs fails, since the probability of each light bulb not to fail is 1-0.02=0.98 the the probability that none of the 13 light bulbs fails is 0.98^13.
Hence, the probability that at least one light bulb fails is 1-0.98^13.
Answer: E.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 13, then according to your logic the probability that the string of light bulbs will fail would be 100*0.02=2, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: E
Question: R is an even integer greater than 300,000 and smaller than 1,000,000. How many numbers can R be?
Options:
A)300,000
B)349,999
C)350,000
D)399,999
E)400,000
Rationale: R 1,000,000-300,000=700,000 integers
700,000/2= 350,000 even integers.
350,000+1 inclusive. But since 1,000,000 and 300,000 are not included.
350,001-2=349,999
B
Answer: B
Question: Four different children have jelly beans: Aaron has 5, Bianca has 7, Callie has 8, and Dante has 13. How many jelly beans must Dante give to Aaron to ensure that no child has more than 1 fewer jelly beans than any other child?
Options:
A) 2
B) 3
C) 4
D) 5
E) 6
Rationale: Since Bianca and Callie are both within 1 jelly bean of each other and Aaron has 5, Dante must provide 3 of his 13 jelly beans so each child has no more than 1 fewer jelly bean than any other child.
Dante + Aaron = 13+5 =18/2 = 9
13-8 = 5 so Dante must provide 5 jelly beans to Aaron.
Answer (D)
Answer: D
Question: A sum of Rs. 125000 amounts to Rs. 16000 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)3%
B)4%
C)5%
D)6%
E)7%
Rationale: S.I. = (16000 - 12500) = Rs. 3500\
Rate = (100 * 3500) / (12500 * 4) = 7%
ANSWER:E
Answer: E
Question: A car covers a distance of 540 km in10 hrs. What is its speed in mps.
Options:
A)40 m/s
B)25 m/s
C)20 m/s
D)15 m/s
E)16 m/s
Rationale: Explanation:
Distance = Speed x Time
Speed = (540/10) = 54 kmph
Spees in mps = 54 x 5/18 = 3 x 5 = 15 mps.
Answer: Option D
Answer: D
Question: How many such three letter passwords can exist?
Options:
A)216
B)26C6 *3
C)(26C6)^3
D)((26C6)^3) *63
E)215
Rationale: 1st ring: 6 out of 26 alphabets can be selected in 26C6 ways.
And is for 2nd and 3rd ring.
Also, these 3 set of 6 letters can be arranged amongst themselves in 63 ways.
Hence, total number of 3 letter passwords = 26C6 * 26C6 *26C6 *63 ways.
ANSWER:D
Answer: D
Question: The average (arithmetic mean)E of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
Options:
A)I only
B)II only
C)III only
D)II and III only
E)None of the above
Rationale: Given :
p + q = EVEN (odd + odd =even)
p + q + s + t = EVEN (even + even = even) nothing more....
(p + q + s + t) / 4 = x
I.
x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.
II.
Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.
III.
As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.
Answer E, None.
Answer: E
Question: What amount does Kiran get if he invests Rs. 18000 at 12% p.a. simple interest for four years?
Options:
A)29893
B)26640
C)29989
D)28800
E)29883
Rationale: Simple interest = (18000 * 4 * 12)/100 = Rs. 8640
Amount = P + I = 18000 + 8640 = Rs. 26640
Answer: B
Answer: B
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 72 kmph. In how much time will the trains cross each other?
Options:
A)80/6 sec
B)80/7 sec
C)88/7 sec
D)80/9 sec
E)82/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35
=80/7 sec.
Answer:B
Answer: B
Question: A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 4120 a year. What is his average monthly income?
Options:
A)2000
B)2010
C)2100
D)2200
E)2300
Rationale: Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 4120 = Rs. 24120
So, Average monthly income = 24120/12 = Rs. 2010
B
Answer: B
Question: The Square of a Positive Number A is divided by 2 and then the Result is Multiplied by 4 if the result is equal to A * 8 then what is the value of A?
Options:
A)4
B)9
C)6
D)3
E)8
Rationale: (A*A)/2*4= 2(A*A)
2(A*A)=8A
2A=8
So the Correct Answer is 4
Answer: A
Question: If w,x,y,z are consecutive positive integers ; then which of the following is always odd?
[1] w*x+(y+2)^2*z
[2] w^x + z^y
[3] 2w^3
Options:
A)2
B)2
C)3
D)1 and 2
E)2 and 3
Rationale: Plug in some numbers
w = 1
x = 2
y = 3
z = 4
Check the options -
[1] w*x+(y+2)^2*z = 1*2 + (3+2)^2 * 4 => 2 + 25*4 = 102{ Not an odd Number }
[2] w^x + z^y = 1^2 + 4^3 => 1 + 64 = 65{ Odd number }
3 2w^3 = 2*1^3 = even
2
A
Answer: A
Question: What is the unit digit in {pow(2114,563) x pow(425,213) x pow(3371,67)}?
Options:
A)0
B)2
C)3
D)5
E)7
Rationale: Solution
Unit digit in pow((2114, 563)
= Unit digit in pow(4,563)
= Unit digit in [pow(pow(4,2),281) x 4]
= Unit digit in (6 x 4)
= 4 Unit digit in pow(425,213)
= Unit digit in pow(5,213)
= 5 Unit digit in pow(3371,67)
= Unit digit in pow(1,67) = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Answer A
Answer: A
Question: A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 27 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
Options:
A)14
B)45
C)54
D)65
E)52
Rationale: Just check the answers and reverse the numbers until you get 27.
52 - 25 = 27
Answer E
Answer: E
Question: A and B can do a piece of work in 3 days. With the help of C they finish the work in 2 days. C alone can do that piece of work in?
Options:
A)6 DAYS
B)5 DAYS
C)4 DAYS
D)3 DAYS
E)2 DAYS
Rationale: C = 1/2 – 1/3= 1/6 => 6 days
Answer:A
Answer: A
Question: Manoj borrowed Rs.3600 from Anwar at 6% p.a. simple interest for three years. He then added some more money to the borrowed sum and lent it to Ramu for the same time at 9% p.a. simple interest. If Manoj gains Rs.824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction, then what is the sum lent by him to Ramu?
Options:
A)22877
B)5455
C)2778
D)6787
E)1771
Rationale: Let the sum lent by Manoj to Ramu be Rs.P.
Amount gained by Manoj = P. 3.9 /100 = 3600.3.6/100 = Rs.824.85
27P = 64800 = 82485
P = (82485 + 64800)/27 = 3055 + 2400 = Rs.5455
Answer: B
Answer: B