divelab/Sys2Bench huggingface dataset:
Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 600. How much did he have with him in the beginning?
Options:
A)s 200
B)s 1500
C)s 300
D)s 450
E)s 550
Rationale: Suppose the amount in the beginning was Rs ’x’
Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3
Money spent on food = 1/5 of 2x/3 = Rs 2x/15
Balance = 2x/3 - 2x/15 = Rs 8x/15
Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5
Therefore 2x/5 = 100 = 1500
ANSWER:B
Answer: B
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
Options:
A)61mph
B)62mph
C)63mph
D)64mph
E)65mph
Rationale: (2*40+3*80)/5 = 64mph
ANSWER:D
Answer: D
Question: x, y, a, and b are positive integers of H. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
Options:
A)24
B)21
C)20
D)17
E)15
Rationale: x, y, a, and b are positive integers of H. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9.Answer: E.
Answer: E
Question: John, a painter, has 9 jars of paint: 4 are white, 2 are yellow, and the rest are brown. John will combine 3 jars of paint into a new container to make a new colour, which he will name according to the following conditions: 1) C1, if the paint contains 2 jars of brown paint and no white paint 2) C2, if the paint contains 3 jars of brown paint. 3) J1, if the paint contains at least 2 jars of white paint 4) J2, if the paint contains exactly 1 jar of white paint What is the probability that the new colour will be a shade of J (J1 or J2)?
Options:
A)42/37
B)84/37
C)21/37
D)74/42
E)37/42
Rationale: the probability that it would be J1 or J2 is same as 1-()probability that it is C1 or C2
For C1-3C2(Brown)*2C1(Yellow)=3*2=6
For C2-3C3(all brown)=1
Total=9C3=84
1-7/84=77/84= 37/42
Answer : E
Answer: E
Question: A sum of money amounts to Rs.6690 after 3 years and to Rs.10,035 after 6 years on compound interest.find the sum.
Options:
A)333
B)4460
C)37687
D)26698
E)2911
Rationale: Explanation:
Let the sum be Rs.P.then
P(1+R/100)^3=6690…(i) and P(1+R/100)^6=10035…(ii)
On dividing,we get (1+R/100)^3=10025/6690=3/2.
Substituting this value in (i),we get:
P*(3/2)=6690 or P=(6690*2/3)=4460
Hence,the sum is rs.4460.
Answer: B) 4460
Answer: B
Question: Arun Kumar, Chennakesavan , Raghu and Krishnan always have discussions on various issues such as politics, international affairs, current affairs, studies etc. Once Raghu posed the following query to other group members:Find the range of real values of x satisfying the inequalities 4x - 5 > 7 and 5x - 14 > 16"
Options:
A)x > 3
B)x > 6
C)x < 3
D)x < 6
E)none
Rationale: 4x - 5 > 7 => 4x > 12 => x > 3 ...(1)
and 5x - 14 > 16 => 5x >30 => x > 6 ...(2)
Since 6 is greater than 3, for both inequalities namely (1) and (2) to be satisfied, x should be greater than 6 or x > 6.
ANSWER:B
Answer: B
Question: A searchlight on top of the watchtower makes 4 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 12 seconds?
Options:
A)1/2
B)2/3
C)1/3
D)1/4
E)1/5
Rationale: The searchlight completes one revolution every 15 seconds.
The probability that the man's area will be lit up is 12/15=4/5.
The probability that he will stay in the dark is 1-4/5=1/5
The answer is E.
Answer: E
Question: John and Steve are speed walkers in a race. John is 16 meters behind Steve when he begins his final push. John blazes to the finish at a pace of 4.2 m/s, while Steve maintains a blistering 3.7 m/s speed. If John finishes the race 2 meters ahead of Steve, how long was John’s final push?
Options:
A)13 seconds
B)17 seconds
C)36 seconds
D)34 seconds
E)51 seconds
Rationale: Let t be the time that John spent for his final push.
Thus, per the question,
4.2t = 3.7t+16+2 ---> 0.5t = 18 ---> t = 36 seconds.
C is the correct answer.
Answer: C
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
Options:
A)1/45
B)1/42
C)1/46
D)1/48
E)1/43
Rationale: 2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer:B
Answer: B
Question: How many words, with or without meaning, can be formed using all letters of the word GOOD using each letter exactly once?
Options:
A)18
B)20
C)22
D)23
E)24
Rationale: The Word GOOD has exactly 4 letters which are all different.
Therefore the number of words that can be formed = Number of permutations of 4 letters taken all at a time.
= P (4, 4) = 4!
= 4 x 3 x 2 × 1
= 24
ANSWER:E
Answer: E
Question: At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
Options:
A)5 min past 7
B)5x6/11 min past 7
C)5x5/22 min past 7
D)5x5/11 min past 7
E)5/22 min past 7
Rationale: Explanation:
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in60/55x 5	min	= 5X 5/11	min.
Required time = 5x 5/11	min. past 7.
Answer is D
Answer: D
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 20 such machines produce in 4 minutes?
Options:
A) 648
B) 1,800
C) 2,700
D) 3,600
E) 64,800
Rationale: 6 machines produce 270 bottles per minute;
1 machine produces 270/6=45 bottles per minute;
20 machines produce 45*20=900 bottles per minute;
In 4 minutes 10 machines produce 900*4=3,600 bottles.
Answer: D.
Answer: D
Question: X divided by 899 gives a remainder 63. What remainder will be obtained by dividing X by 29?
Options:
A)100598
B)10052
C)100528
D)10057
E)100182
Rationale: ANSWER: D
Answer: D
Question: Twelve men can complete a piece of work in 32 days. The same work can be completed by 16 women in 36 days and by 48 boys in 16 days. Find the time taken by one man, one woman and one boy working together to complete the work?
Options:
A)(64 * 36)/13 days
B)(44 * 36)/23 days
C)(64 * 39)/13 days
D)(84 * 36)/13 days
E)(61* 36)/13 days
Rationale: 12 men take 32 days to complete the work.
One man will take (12 * 32) days to complete it.
Similarly one woman will take (16 * 36) days to complete it and one boy will take (48 * 16) days to complete it.
One man, one woman and one boy working together will complete = 1/(12 * 32) + 1/(16 * 36) + 1/(48 * 16)
= 1/(4 * 3 * 16 * 2) + 1/(16 * 4 * 9) + 1/(16 * 3 * 4 * 4)
= 1/64(1/6 + 1/9 + 1/12) = 1/64 * 13/36 of the work in a day.
They will take (64 * 36)/13 days to complete the work working together.
Answer: A
Answer: A
Question: A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing
speed in sƟll water is
Options:
A)4 kmph
B)5 kmph
C)6 kmph
D)7 kmph
E)None of these
Rationale: Explanation:
Rate upstream = (750/675) = 10/9 m/sec
Rate downstream (750/450) m/sec = 5/3 m/sec
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.
= 25/18 m/sec
= (25/18)*(18/5) kmph
= 5 kmph
Answer: B
Answer: B
Question: There are 5 men and 11 women. In how many ways one can select a group of 6 with at-least 3 men?
Options:
A)1935
B)1936
C)1937
D)1938
E)1939
Rationale: 5c3*11c3+5c4*11c2+5c5*11c1=1936
ANSWER:B
Answer: B
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 60 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)480
B)160
C)320
D)192
E)240
Rationale: Four members worked in ration 2:3:5:6, hence as everyone mentioned, individual work could be taken as 2x, 3x,5x, and 6x. Also this gives us total work as 16x.
But we are told that one of these individual works is 60hrs. hence, possible scenarios, if
(1)2x =60 => 16x = 480 (2) 3x =60 => 16x = 320 (3) 5x =60 => 16x = 192 (4) 6x =60 => 16x = 160
Hence Answer is E
Answer: E
Question: A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)270
B)278
C)268
D)266
E)121
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 870 = 270
Answer: A
Answer: A
Question: Laura has a deck of standard playing cards with 12 of the 72 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
Options:
A)1/4
B)1/5
C)5/26
D)12/42
E)1/6
Rationale: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.
If there is no replacement then how is the (P) that the 10th card is 12/72 ??
there are many cases here to be considered here if there is no replacement such as:
H- Denotes heart X-may be any diamond, spade or club.
1. HXXXXXXXXH
2. HHXXXXXXXH
3. HHHXXXXXXH
.
.
.
.
.
9. HHHHHHHHHH
10. XXXXXXXXXH
All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.
For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 12/72 = 1/6 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....
E
Answer: E
Question: What is the least number which should be added to 2597 so that the sum is exactly divisible by 5, 6, 4, and 3?
Options:
A)17
B)23
C)26
D)35
E)43
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
When dividing 2597 by 60, the remainder is 17.
The number to be added = 60 - 17 = 43.
The answer is E.
Answer: E
Question: The age of a person is thrice the total ages of his 2 daughters. 0.5 decades hence, his age will be twice of the total ages of his daughters. Then what is the father’s current age?
[0.5 Decades = 5 Years]
Options:
A)45 years
B)55 years
C)42 years
D)46 years
E)52 years
Rationale: A
45 years
Let, Total of current ages of the 2 daughters is A years.
Then, father’s current age = 3A years.
(3A + 5) = 2 (A +10)
3A + 5 = 2A + 20
A = 15
Therefore, father’s current age = 45 years.
Answer: A
Question: Rerty traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different.
Options:
A)z=3x
B)x=3z
C)y=2x
D)x=2y
E)y=3x
Rationale: Rerty Travelled for x,y and for z min.
Total Time : x + y + z
Which is equal to : 3y
Equating both sides we get
x+y+z = 3y
=> x+z =2y ........ Eqn 1
Looking out at options
D Says x =2y
Using it in Eqn 1
2y + z = 2y
=> Z = 0 mins, Which I guess is not possible.
The Ans isD
Answer: D
Question: Morgan Goldman has 5 Senior Managing Directors and 5 Managing Directors. Each investment banking deal requires the guidance of three managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Morgan Goldman possibly provide guidance for?
Options:
A) 16
B) 36
C) 110
D)154
E) 210
Rationale: P(at least 1 S D) = P(Total) - P(0 Senior Director)
=10C3 - 5C3
= 110
Answer: C
Question: A man invested Rs. 50000 at the rate of 5% p.a. for the first three years, 8% p.a.for the next five years and 10% p.a.for the period beyond eight years. At the end of eleven years, he want to distribute total money among his four sons, How much money will each son get?
Options:
A)30000
B)25375
C)28680
D)32000
E)23125
Rationale: Let the interest be i. Then,
(50000×3×5/100)+(50000×5×8/100)+(50000×3×10/100)=i
⇒ 7500+20000+15000= i
⇒ i = 42500
Total money = 42500+50000 = 92500
Each son will get = 92500/4 = 23125
Answer :E
Answer: E
Question: A man can row 10 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man?
Options:
A)6.24 km
B)6 km
C)9.86 km
D)5.66 km
E)10 km
Rationale: M = 10
S = 1.2
DS = 11.2
US = 8.8
x/11.2 + x/8.8 = 1
x = 4.93
D = 4.93 * 2 = 9.86
ANSWER:C
Answer: C
Question: What is his percentage profit made by Nick if he purchased 10 dozen pens at Rs. 25 per dozen. He sold 3 dozens at 8% profit and the remaining 7 dozens with 14% profit?
Options:
A)15.2%
B)17.2%
C)12.2%
D)11.2%
E)13.2%
Rationale: Explanation :
C.P of 10 dozens = Rs.(25 x 10) = Rs.250
C.P of 3 dozens = Rs. (25 x3) = Rs. 75.
C.P of 7 dozens =Rs. (25 x7) = Rs. 175
profit on 3 dozen at 8% = 8/100*75 = 6
profit on 7 remaining dozen at 14% = 14/100*175 = 24.5
total profit = 6 + 24.5 = 30.5
% profit = ?/100*250 = 30.5
= 12.2%
Answer : C
Answer: C
Question: Find the number of zeroes in 58! (58 factorial)
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: no of zeroes is
58/5=11
11/5=2
11+2=13
ANSWER:B
Answer: B
Question: The contents of a certain box consist of 24 lemons and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be lemons?
Options:
A) 24
B) 26
C) 30
D) 46
E) 50
Rationale: lemons = ( lemons + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Answer: B
Question: Cost of an item is Rs 12.60 & profit is 10% over selling price what is the selling price
Options:
A)12.86
B)13.86
C)14.86
D)15.86
E)16.86
Rationale: Profit=( SP-CP/CP )*100
CP=12.60
(SP-12.60)/12.60*100 =10
SP=13.86
ANSWER:B
Answer: B
Question: In what ratio should a variety of rice costing Rs. 7 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:
A)5/6
B)5/2
C)5/1
D)5/3
E)7/6
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation, x/y
= (8.75 - 7.50) / (7.50 - 7) =5/2
Answer: B
Answer: B
Question: Can you complete below number series by replacing "?" with the correct number.
10 # 10 # 20 # ? # 110 # 300 # 930
Options:
A)35
B)25
C)45
D)55
E)75
Rationale: Pattern goes like
10
10 * 0.5 + 5 => 10
10 * 1.0
+ 10 => 20
20 * 1.5 + 15 => 45(Ans)
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930
Correct answer is C)45
Answer: C
Question: Before being simplified, the instructions for computing income tax in Country R were to add 2 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 A?
Options:
A)50+A/200
B)50+3A/100
C)50+A/40
D)100+A/50
E)100+3A/100
Rationale: the simplified formula for computing the income tax, in Country R's currency, for a person in that country
annual income is A:50+A/40
ANSWER:C
Answer: C
Question: v, q, and r are positive integers. If v, q, and r are assembled into the six-digit number vqrvqr, which one of the following must be a factor of vqrvqr?
Options:
A) 23
B) 19
C) 17
D) 7
E) none of the above
Rationale: One short way -
vqrvqr = 1000vqr + vqr = (1000+1)vqr = 1001vqr
Therefore any factor of 1001 is a factor of vqrvqr
7 is a factor of 1001
So D
Answer: D
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
Options:
A)2387
B)2978
C)3972
D)2671
E)1871
Rationale: Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
Answer: C
Answer: C
Question: The number 86 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
Options:
A)17
B)16
C)15
D)14
E)13
Rationale: 7^2+6^2+1^2=49+36+1 = 86
7+6+1 =14
Hence answer is D
Answer: D
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
Options:
A)5729
B)5760
C)2889
D)2870
E)2799
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760.Answer: B
Answer: B
Question: When the integer n is divided by 8, the remainder is 5. Which of the following is NOT an even number?
Options:
A)n + 3
B)n/2 + 3.5
C)n – 3
D)3n + 1
E)5n + 2
Rationale: Given number = N =8p+5 ---> the number N is odd.
Thus ,
A. n + 3
n+3 = odd + odd = even. Thus not correct.
B. n/2 + 3.5
As n is odd, thus n/2 = abc.5 (where c = even) ---> abc.5+3.5 = abc+3+0.5+0.5 = even+odd+1= odd+1=even. Thus not correct.
C. n – 3
n-3 = odd - odd = even. Thus not correct.
D. 3n + 1
As n =odd, 3n=odd and 3n+1 = odd + odd = even. Thus not correct.
E. 5n + 2
As n =odd, 5n= odd --->5n+2 = odd + even = odd. Thus correct. ANSWER:E
Answer: E
Question: P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 150 days, in how many days can R alone complete the remaining work?
Options:
A)50 days
B)75 days
C)120 days
D)150 days
E)80 days
Rationale: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days
P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 400 days
P works for 60 days--> 60/200 work done => 30%
Q works for 150 days--> 150/250 work done => 60%
30% work left ... R alone will take 30% * 400 = 120 days
Answer is (C)
Answer: C
Question: The sum of first eight prime numbers is?
Options:
A)12
B)23
C)24
D)77
E)30
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19) = 77.
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.
D
Answer: D
Question: It takes Joey the postman 1 hours to run a 2 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 5 mile/hour, what is the speed with which Joey returns?
Options:
A)10
B)12
C)13
D)14
E)15
Rationale: let his speed for one half of the journey be 2 miles an hour
let the other half be x miles an hour
now,
avg speed =5 mile an hour
2*2*x/2+x=5
4x=5x+10=>x=10
A
Answer: A
Question: Find the odd man out. 12, 24, 36, 48, 61, 72, 84
Options:
A)15
B)25
C)61
D)90
E)115
Rationale: Explanation :
All except 61 are multiples of 7
Answer : Option C
Answer: C
Question: A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1540 are infected, how manyworkersinhabit the colony?
Options:
A)1500
B)2500
C)2750
D)3000
E)3500
Rationale: From two question we get wo equations:
(1) 0,3s + 0,14w = 1540
(2) s + w = 7000
From (2) we get w=7000-s
In (1) 0,3s + 980-0,14s= 1540
0,16s=560
56000:16= 3500 =s
In (2) 3500 + w = 7000
w= 3500 E
Answer: E
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Options:
A)50400
B)5040
C)5004
D)7007
E)7004
Rationale: In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters =	7!/2!	= 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in	5!/3!	= 20 ways.
Required number of ways = (2520 x 20) = 50400.
ANSWER A
Answer: A
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum mark is
Options:
A)600
B)500
C)400
D)300
E)800
Rationale: The student got 125 marks and still failed by 40 marks
= 125+40 = 165
therefore 33% of the total marks = 165
100% of the total = 165*100/33=55
max mark = 500
ANSWER B
Answer: B
Question: Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 30 phone numbers by using the readable digits followed by 30 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
Options:
A)1/9
B)10/243
C)1/27
D)10/271
E)1/1000000
Rationale: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 30/(9*9*3+9*3) = 1/9.
Answer:A.
Answer: A
Question: trees of heights 30 and 40 sepatated by a river. fish in the river is at equal dis from top of the trees where two birds are there.ratio of the distances from fish to the root of the trees?
Options:
A)4:3
B)1:2
C)2:1
D)3:4
E)1:3
Rationale: 40/30 is the ratio of distance from fish to root of trees
4:3
ANSWER:A
Answer: A
Question: Jim Pete’s only source of income comes from his job as a question writer. In this capacity, Jim earns a flat salary of $200 per week plus a fee of $9 for every question that he writes. Every year, Jim takes exactly two weeks of unpaid vacation to visit his uncle, a monk in Meivazhi Salai, and get inspired for the next year. If a regular year consists of 52 weeks and the number of questions that Jim wrote in each of the past 5 years was an odd number greater than 20, which of the following could be Jim’s median annual income over the past 5 years?
Options:
A)$22,474
B)$25,673
C)$27,318
D)$28,459
E)$31,227
Rationale: Okay u just need less than one min to answer this question. any odd number greater than 20 means that that last digit must be 1,3,5,7, or 9. 9$ per week for every question. So (odd)(odd) will give odd digit. A and C out. (50 weeks) (200) = 10,000. subtract this amount from option B, D and E and u will find that only option D is divisible by 9 (once 10,000 is subtracted from 28459) so its the right choice..D
Answer: D
Question: If T divided by B equals 9.16 what is a possible remainder?
Options:
A)8
B)9
C)2
D)6
E)5
Rationale: With the decimal being 16/100, the simplest form is 4/25. If the divisor is a multiple of 25, the remainder must be a multiple of 4. The only number that is so is 8. Answer A.
Answer: A
Question: A train 200 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)11
B)10
C)5
D)9
E)8
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [200 * 3/55] sec = 11 sec
ANSWER:A
Answer: A
Question: If |4x+10| = 46, what is the sum of all the possible values of x?
Options:
A)2
B)-2
C)4
D)-5
E)6
Rationale: There will be two cases
4x+10= 46 or 4x+10 = -46
=> x =9 or x= -14
sum of both the values will be -14 +9 = -5
Answer is D
Answer: D
Question: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the seventh digit of p, counting right to left from the units digit?
Options:
A)1
B)2
C)3
D)6
E)9
Rationale: C
Sum of unit digits of first 30 terms = 60
Sum of tens digits of first 30 terms = 58
Sum of thousands digits of first 30 terms = 56
and so on..
p1 = 0
p2 = (6+58) = 4
p3 = (6+56) = 2
p4 = (6+54) = 0
p5 = (6+52) = 8
p6 = (5+50) = 5
p7 = (5+48) = 3
ANSWER: C
Answer: C