divelab/Sys2Bench huggingface dataset:
Question: Ten years ago, a mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of the daughter is
Options:
A)22
B)21
C)24
D)20
E)19
Rationale: Let the mother’s present age be ’x’
Let the daughter’s age be ’y’;
10 years ago; (x - 10) = 4(y - 10) or x - 4y = - 30.. (1)
10 years later; (x + 10) = 2(y + 10) or x - 2y = 10.. (2)
Solving (1) & (2)
y = 20
ANSWER:D
Answer: D
Question: In what time will Rs.1000 become Rs.1331 at 10% per annum compounded annually
Options:
A)2 Years
B)3 Years
C)4 Years
D)5 Years
E)None of these
Rationale: Explanation:
Principal = Rs.1000;
Amount = Rs.1331;
Rate = Rs.10%p.a.
Let the time be n years then,
1000(1+10100)n=1331(1110)n=13311000(1110)3=13311000
So answer is 3 years
Answer: B
Answer: B
Question: The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 13 km/hr respectively. They will meet for the first time in?
Options:
A)50min
B)33min
C)35min
D)25min
E)20min
Rationale: Clearly, the two will meet when they are 1000 m apart
To be 20+13 = 33 km apart, they take 1 hour
To be 1000 m apart, they take 33 * 1000/1000 = 33 min.
Answer is B
Answer: B
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
A)63
B)25
C)40
D)65
E)98
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
ANSWER A
Answer: A
Question: From the below series find the remainder? 1201 × 1203 ×1205 × 1207 is divided by 6?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Answer: A
Question: If 0 < a < b and k = (2a + 12b)/b , which of the following must be true?
Options:
A)k < 2
B)k < 7
C)k < 9
D)k > 9
E)k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a<b, you get k = (2+24)/2 = 13. This eliminates all but option E , making it the correct answer.
Answer: E
Question: A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 2 new workers. How many different ways can she assign the new workers?
Options:
A)23760
B)47520
C)33000
D)48600
E)54000
Rationale: whatever : my take selecting team of 2 out of 12 to assign to the shifts = 12C2 = 66 ways.
now 2 out of 12 means total of 6 group possible.
so putting them in shifts = counting methode: first, second, third, alt , alt
= 6*5*4*3*2*1 = 720
here alt and alt are the same: so 720/2 = 360 ways.
total ways of selecting = (selecting 2 out of 12)*arranging those teams in shifts
= 66*360 = 23760
Ans: A
Answer: A
Question: In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 5 and a y-intercept of -5. If the two lines intersect at the point (a,b), what is the sum a+b?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The equation of Line A is y = -x + 1
The equation of Line B is y = 5x - 5
5x - 5 = -x + 1
x = 1
y = 0
The point of intersection is (1,0) and then a+b = 1.
The answer is B.
Answer: B
Question: If A= {2, 4, 6}, B= {1, 2, 5, 7}, and C= {2, 3, 4, 6}. Find A-(B U C)
Options:
A){1 , 2}
B){2 ,3 ,5 }
C){ }
D){5 }
E)None of these
Rationale: Explanation :
A= {2, 4, 6},
B= {1, 2, 5, 7},
C = {2, 3, 4, 6}
Now,(B U C) = {1, 2, 5, 7} U {2, 3, 4, 6} = {1,2,3,4,5,6,7}
A-(B U C) = {2, 4, 6} - {1,2,3,4,5,6,7} = { }
Hence (C) is correct answer.
Answer : C
Answer: C
Question: A radio station has to choose two days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
Options:
A)9
B)15
C)21
D)35
E)56
Rationale: Behind the story, we are really being asked to evaluate 7C2. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C2, the third entry of the seventh row, is 21. Answer = C.
Answer: C
Question: John has on his shelf four books of poetry, four novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one poetry?
Options:
A)1/2
B)2/5
C)3/10
D)7/20
E)16/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 4/10*4/9 + 4/10*4/9 = 16/45.
Answer: E.
Answer: E
Question: How many trailing Zeroes does 53! + 54! have?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: 53! + 54! = 53! + 54 * 53!
= 53! (1 + 54)
= 53! * 55
Number of trailing 0s in 53! = number of 5s in the expansion of 53!
= 10 + 2 = 12
There is 1 more 5 in 55.
Hence, total number of trailing 0s = 12 + 1 = 13
Answer (B)
Answer: B
Question: A person took some amount with some interest for 5 years, but increase the interest for 1%, he paid Rs.250/- extra, then how much amount he took?
Options:
A)Rs.5500/-
B)Rs.6000/-
C)Rs.4000/-
D)Rs.5000/-
E)None of these
Rationale: Explanation:5 years = Rs.250/-year = 250/5Rate of Interest = 1%100/1% × 250/5 = Rs.5000/-P = Rs.5000/- Answer: Option D
Answer: D
Question: One millisecond is 0.001 of a second. The costs for a single run of a computer program are $1.07 for operating-system overhead, $0.019 per millisecond of computer time, and $4.35 for the mounting of a data tape. What is the total of these three costs for 1 run of a program that requires 1.5 seconds of computer time ?
Options:
A) $7.15
B) $8.87
C) $33.92
D) $35.57
E) $39.62
Rationale: Operating system overhead for 1 run = 1.07 $
Mounting of data tape = 4.35$
Cost per 1 millisecond of computer time = .019 $
Total cost of 1 run of a program that requires 1.5 seconds of computer time
= 1.07 + (.019*1500) + 4.35
=1.07 + 28.5 + 4.35
= 33.92$
Answer C
Answer: C
Question: Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 40 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast?
Options:
A)10%
B)12%
C)15%
D)17%
E)20%
Rationale: Lets assume that candidate got 40% votes and total votes is 100.
Candidate won = 40
Remaining = 60
To get 50%, candidate requires 10 votes from 100 which is 10% and 10 votes from 60.
10/60 = 1/6 = .166 = 16.67%
Which is approx 17%. Hence the answer is D
Answer: D
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 36 hours respectively. The ratio of their speeds is
Options:
A)4:1
B)4:2
C)4:5
D)6:3
E)3:6
Rationale: Ratio of their speeds = Speed of first train : Speed of second train
= √36−−√9
= 6:3
Answer is D.
Answer: D
Question: If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+69)=?
Options:
A)3675
B)3575
C)3475
D)3375
E)3275
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 69=1+(n-1)2
=> n=35
Use value of n in (1)
then,
Sn = (35/2)(1+69) = 1225
Ans:- 3(Sn) = 3675
Answer : A
Answer: A
Question: The length of a train and that of a platform are equal. If with a speed of 108 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)227
B)299
C)276
D)750
E)900
Rationale: Speed = [108 * 5/18] m/sec = 30 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 30 è x = 30 * 60 / 2 = 900
Answer: E
Answer: E
Question: Given that E and F are events such that P(E) = 0.16, P(F) = 0.4 and P(E n F) = 0.4,
find P (E|F) and P(F|E)
Options:
A)1/2
B)1/7
C)1/4
D)1/3
E)1/5
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 0.4/0.4 = 1
P(F|E) = P(EnF)/P(E) = 0.4/0.16 = 1/4.
C
Answer: C
Question: In 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date February 12, 1995 is a Wednesday, then which one of the following would the date February 12, 1996 be?
Options:
A)Thursday
B)Friday
C)Saturday
D)Sunday
E)Monday
Rationale: From the information given, Feb 12, 1996 is 366 days after Feb 12, 1995.
366 days = 52 weeks and 2 more days. Therefore if Feb 12, 1995 is a Wednesday, then Feb 12, 1996 is Wednesday + 2 days = Friday
Answer: B
Answer: B
Question: In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
Options:
A)2 hrs
B)3 hrs
C)5 hrs
D)6 hrs
E)4 hrs
Rationale: A
Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
Answer: A
Question: In a workshop there are 4 kinds of beds, 2 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
Options:
A)168.
B)80.
C)56.
D)48.
E)72.
Rationale: ways to select one shelf = 2
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 7+2 = 9
ways to select all of them together = 2*4*9 = 72
Hence, E is the answer.
Answer: E
Question: What is the average of first 21 multiples of 6 ?
Options:
A)A)66
B)B)77
C)C)79
D)D)81
E)E)82
Rationale: Required average = 6(1+2+....+21) / 21
(6/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 66
A
Answer: A
Question: Machine A and machine B are each used to manufacture 550 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?
Options:
A)5.5
B)6.6
C)60
D)100
E)110
Rationale: time taken by B = t
time taken by A = t+10
qty produced by A = q
qty produced by B = 1.1 q
for B: t(1.1q) =550
qt=500
for A: (t+10)(q) =550
qt+10q=550
500+10q=550
q=5
so A can produce 5/hour.
then B can produce = 5(1.1)=5.5/hour.
A
Answer: A
Question: Which of the following numbers is two more than the square of an odd integer?
Options:
A)14,173
B)14,361
C)15,131
D)15,737
E)15,981
Rationale: If a square has an odd unit's digit, then its ten's digit must be even.
Only 15,131-2 = 15,129 satisfies this condition.
The answer is C.
Answer: C
Question: How many positive integers S less than 20 are either a multiple of 2, an odd multiple of 9, or the sum of a positive multiple of 2 and a positive multiple of 9 ?
Options:
A)19
B)18
C)17
D)16
E)15
Rationale: We're asked to deal with the positive integers LESS than 20. There are only 19 numbers in that group (1 to 19, inclusive). We're asked to find all of the numbers that fit one (or more) of the given descriptions. Looking at the answer choices, we have every value form 15 to 19, inclusive, so most (if not all) of the numbers from 1 to 19 fit one (or more) of the descriptions. How long would it take you to find the ones that DON'T fit.....?
The first several should be pretty easy to find - the prompt wants us to focus on multiples of 2 and 9 (and sums of those multiples). So what ODD numbers are less than 9?
1, 3, 5, 7
None of these values fit the given descriptions. That's 4 out of 19 that we know for sure do NOT fit. 19 - 4 = 15 = E
Answer: E
Question: Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 16 km apart, if they walk in the same direction?
Options:
A)5hours
B)6hours
C)8hours
D)16hours
E)12hours
Rationale: To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 16 =8 hours
Answer is C
Answer: C
Question: John went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)19.7
C)19.9
D)20.9
E)21
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B
Answer: B
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother six years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2 years
B)4 years
C)6 years
D)7 years
E)8 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 6) years = 44 years.
Required difference = (44 - 36) years = 8 years.
Answer: Option E
Answer: E
Question: A group of tourists wants to visit only two or three of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
Options:
A)24
B)28
C)32
D)36
E)40
Rationale: The number of ways to choose two cities is 4C2=6.
The number of itineraries for each pair of 2 cities is 2!.
So the number of itineraries to two cities is 6*2!=12.
The number of ways to choose three cities is 4C3=4.
The number of itineraries for each group of 3 cities is 3!.
So the number of itineraries to three cities is 4*3!=24.
The total number of itineraries is 12+24=36.
The answer is D.
Answer: D
Question: The difference between a number and its two-fifth is 510. What is 12% of that number?
Options:
A)58
B)110
C)76
D)102
E)86
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
12% of 850 = 102.
Answer:D
Answer: D
Question: A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then?
Options:
A)144
B)121
C)256
D)320
E)169
Rationale: If each of 6 tractors ploughed 120 hectares a day and they finished the work in 4 days, then the whole field is: 120⋅6⋅4=720⋅4=2880 hectares. Let's suppose that each of the four tractors ploughed x hectares a day. Therefore in 5 days they ploughed
5⋅4⋅x=20⋅x hectares, which equals the area of the whole field, 2880 hectares.
So, we get 20x=2880
x=288020=144. Hence, each of the four tractors would plough 144 hectares a day.
So answer is A
Answer: A
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 10 pages.
Options:
A)8
B)10
C)12
D)4
E)16
Rationale: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(10/2.5)=4 hrs
ANSWER:D
Answer: D
Question: What is the absolute value of twice the difference of the roots of the equation W=5y^2 − 20y + 15 = 0 ?
Options:
A) 0
B) 1
C) 2
D) 3
E) 4
Rationale: W=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.
Answer: E.
Answer: E
Question: The product Z of two prime numbers is between 15 and 36. If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 8 but less than 24, then what is Z?
Options:
A)35
B)33
C)28
D)21
E)15
Rationale: The smallest possible product is 33 which is 3*11.
All other products are too big.
The answer is B.
Answer: B
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction Z of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
Options:
A)1/(3x)
B)3x/(x-3)
C)(x – 3)/(3x)
D)x/(x-3)
E)(x-3)/x
Rationale: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete Z=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Answer: C
Question: The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100% capacity, how long will it take to drain the pool?
Options:
A)1400
B)1600
C)1800
D)1500
E)2000
Rationale: volume of pool = 80*150*10 cu.ft ,100% full = 60*100*10*1 cu.ft water is available to drain.
draining capacity =60 cu.ft /min therefore time taken = 80*150*10*1/ 60 min= 2000 min
E
Answer: E
Question: If one-third of one-fourth of a number is 25, then three-tenth of that number is:
A. 35
Options:
A)23
B)90
C)26
D)54
E)01
Rationale: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 25
Number is 300 then 300 Ã— 3/10 = 90
Answer: B
Answer: B
Question: 13 sheeps and 9 pigs were bought for Rs. 1291.85.If the average price of a sheep be Rs. 74. What
is the average price of a pig.
Options:
A)Rs. 26.65
B)Rs. 36.55
C)Rs. 35.65
D)Rs. 36.65
E)Rs. 33.65
Rationale: Average price of a sheep = Rs. 74
: . Total price of 13 sheeps
= (74*13) = Rs. 962
But, total price of 13 sheeps and 9 pigs
= Rs. 1291.85
Total price of 9 pigs
= Rs. (1291.85-962) = Rs. 329.85
Hence, average price of a pig
= (329.85/9) = Rs. 36.65
Answer is D.
Answer: D
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is ?
Options:
A)17/27
B)17/25
C)17/17
D)17/88
E)17/22
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 =17/25.
Answer:B
Answer: B
Question: What percent is 36 paisa's of 12 rupees?
Options:
A)3 %
B)4 %
C)5 %
D)6 %
E)7 %
Rationale: 12 Rupees = 1200paisa's
36/1200 × 100 = 3/12
12/3 = 3 %
A
Answer: A
Question: add 11% of 36 and 12% of 64.
Options:
A)9.5
B)10.5
C)11.5
D)12
E)15
Rationale: 11% of 36 + 12% of 64
36*11/100+64*12/100
3.9+7.6=11.5
answer C
Answer: C
Question: Without stoppages, a train travels certain distance with an average speed of 400 km/h, and with stoppages, it covers the same distance with an average speed of 360 km/h. How many minutes per hour the train stops ?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Due to stoppages, it covers 40 km less .
Time taken to cover 40 km = 40â„400h = 1â„10h
= 1â„10 Ã— 60 min = 6 min
Answer D
Answer: D
Question: 30 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Options:
A)625
B)870
C)576
D)676
E)700
Rationale: we can go in any bus out of the 30 buses.
Hence He can go in 30 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 29 ways.
Total number of ways = 30 x 29 = 870
ANSWER:B
Answer: B
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 240 envelopes
Options:
A)6 minutes
B)5 minutes
C)7 minutes
D)3 minutes
E)4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 240 envelopes they will take 240/60 mins. i.e., 4 mins.
ANSWER:E
Answer: E
Question: A man buys 25 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 25 lts of another mixture with 30% of liquid. What is the % of water in the new mixture?
Options:
A)55
B)82
C)73
D)75
E)85
Rationale: 20% in 25 lts is5. So water = 25-5 = 20 lts. 30% of 25 lts =7.5. So water in 2nd mixture = 25-7.5 =17.5 lts. Now total quantity = 25 + 25 =50 lts. Total water in it will be 20 + 17.5= 37.5 lts. % of water = (100*37.5)/50 = 75.
ANSWER:D
Answer: D
Question: 1300 boys and 700 girls are examined in a test; 52% of the boys and 43% of the girls pass. The percentage of the total who failed is ?
Options:
A)A)63.3%
B)B)52.4%
C)C)81.2%
D)D)51.15%
E)E)69.1%
Rationale: Total number of students = 1300+700 = 2000
Number of students passed = (52% of 1300+43% of 700) = 676+301 = 977
number of failures = 1023*100/2000= 51.15%
Answer is D
Answer: D
Question: he population of a city is 160,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
Options:
A)1797787
B)1797723
C)179776
D)179728
E)179718
Rationale: Population after n years = P [1 + (R/100)]2
Population after 2 years = 160000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 179776
ANSWER: C
Answer: C
Question: How many positive integers less than 50 are multiples of 2 but NOT multiples of 5?
Options:
A)4
B)6
C)8
D)10
E)20
Rationale: IMO the answer is C (8 numbers)
The LCM of 2 and 5 is 10.
If x <50 and x is divisible by 2 not by 5 --> x is NOT divisible by 10.
From 1--> 50, we have 5 numbers which is divisible by 10: 10, 20, 30, 40, 50.
From 1-->50, we have (50-2)/2 +1 = 25 numbers divisible by 2.
Therefore, our answer is 25-5 = 20 numbers.
E
Answer: E
Question: Rewrite (10^38) – 85 as a base 10 integer, what is the sum of the digits in that integer?
Options:
A)354
B)357
C)330
D)370
E)360
Rationale: We know that (10^38) is ending 00, so (10^38) – 85=9....9915
total number of digits in (10^38) – 85 is 38, or 36 digits of 9 and two digits 1 and 5.
answer choice is 36*9+6=330
Answer is C 330
Answer: C
Question: JC has to visit at least 2 European cities on his vacation trip. If he can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can JC create?
Options:
A)12
B)36
C)48
D)60
E)72
Rationale: The question asks the different itineraries, and we need to count the order. For example, visiting city A first and visiting city B later is different from visiting city B first and visiting city A later.
To visit 2 cities from 4 cities, there are 4Ã—3=124Ã—3=12 different itineraries
To visit 3 cities from 4 cities, there are 4Ã—3Ã—2=244Ã—3Ã—2=24 different itineraries
To visit 4 cities from 4 cities, there are 4Ã—3Ã—2Ã—1=244Ã—3Ã—2Ã—1=24 different itineraries
The total different itineraries are 12+24+24=6012+24+24=60 different itineraries.
Answer: D
Answer: D
Question: If two of the four expressions a + b , b + 7b, a - b, and 7a - b are chosen at random, what is the probability that their product will be of the form of a^2-(xb)^2, where x is an integer?
Options:
A)1/2
B)1/7
C)1/6
D)1/8
E)1/5
Rationale: Total number of expressions if 2 are multiplied = 4C2 = 4!/2!*2! = 6
now we have to find the expressions that are in form of x^2 - (by)^2
one is (a+b)(a-b) = a^2 - (1b)^2
If you see any other combination we are always going to have one term of ab since 7a and 7b are there, so there can be only one type of combination like this.
therefore, probablity is 1/6
Answer : C
Answer: C