divelab/Sys2Bench huggingface dataset:
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance?
Options:
A)$3.00
B)$3.20
C)$3.40
D)$3.60
E)$3.80
Rationale: x = 3x/5 + 1/3*2x/5 + 96
4x/15 = 96
x = $3.60 = $3.60
The answer is D.
Answer: D
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
Options:
A)7%
B)5%
C)8%
D)6%
E)9%
Rationale: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%
Answer:B
Answer: B
Question: If a is an integer greater than 9 but less than 26 and b is an integer greater than 14 but less than 31, what is the range of a/b?
Options:
A)1
B)1/2
C)5/6
D)2/3
E)4/3
Rationale: Range of a/b = max(a/b) - min(a/b)
to get max(a/b) => max(a)/min(b) = 25/15
to get min(a/b) => min(a)/max(b) = 10/30
Range = 25/15 - 10/30
= 4/3
Answer: E
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Options:
A)2400 m^2
B)2420 m^2
C)2520 m^2
D)2600 m^2
E)2630 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: The ratio of the present ages of Giri and Hari is 5:8. 12 years hence, the ratio of their ages will be 11:14. Find the difference in their present ages?
Options:
A)7 years
B)6 years
C)9 years
D)5 years
E)4 years
Rationale: Let the present ages of Giri and Hari be 5x and 8x years respectively.
(5x + 12)/(8x + 12) = 11/14
70x + 168 = 88x + 132 => x = 2
Difference in their ages will be the same at all times.
This difference = Difference of their present ages
=> 8x - 5x = 3x => 6 years
Answer: B
Answer: B
Question: A trader bought a car at 30% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)18%
B)26%
C)12%
D)32%
E)15%
Rationale: Original price = 100
CP = 70
S = 70*(180/100) = 126
100 - 126= 26%
Answer: B
Answer: B
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod?
Options:
A)22.8 kg
B)26.6 kg
C)28 kg
D)26.5 kg
E)None of these
Rationale: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 7 :: 42.75 : x
=> 11.25 x x = 7 x 42.75
=> x = (7 x 42.75) / 11.25
=> x = 26.6
Answer : B
Answer: B
Question: The radius of a semicircle is 7. What is the approximate perimeter of the semicircle?
Options:
A)36
B)25
C)15
D)28
E)37
Rationale: perimeter of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*7 + 2*7 = 35.98 approximately 36
answer A
Answer: A
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
A)2
B)3
C)76
D)6
E)1
Rationale: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins.Answer: B
Answer: B
Question: Determine the value of 27/31+54/62
Options:
A)86/31
B)87/31
C)88/31
D)89/31
E)none
Rationale: Solution:
Both fractions should be reduced before performing arithmetic operations. We get 27/31+2.27/2.31=27/31+27/31=2(27/31)=89/31
Answer D
Answer: D
Question: Praveen age after 10years will be 3 times his age 3years back. what is the present age of Chris?
Options:
A)20
B)25
C)10
D)30
E)15
Rationale: Chris present age= x
after 10years = x+10
3years back = x-3
x+10= 3(x-3)
x=20
Answer is A
Answer: A
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8310/-. Find out the amount that he borrowed.
Options:
A)s. 5266
B)s. 5396
C)s. 5228
D)s. 5218
E)s. 52192
Rationale: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8310 = P + (54P/100)
8310 = (100P + 54P)/100
8310 = 154P/100
P = (8310 * 100)/154 = Rs. 5396.104
ANSWER: B
Answer: B
Question: The total age of A and B is 11 years more than the total age of B and C. C is how many years younger than A.?
Options:
A)16
B)12
C)11
D)20
E)10
Rationale: (A+B)-(B-C)=11
A-C=11
Answer is C
Answer: C
Question: When 17 is divided by positive integer x, the remainder is 1. For how many values of x is this true?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: When 17 is divided by x, the remainder is 1 i.e. 1 orange left over after grouping, so x must be greater than 1.
It also means that 16 is completely divisible by x.
Factors of 16 are 1, 2, 4, 8, 16.
Out of these, x can be 2, 4, 8, and 16.
Answer (D).
Answer: D
Question: In an election, candidate A got 80% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?
Options:
A)355600
B)380800
C)356500
D)356800
E)357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 80 %
Therefore, the number of valid votes polled in favour of candidate A = 80 % of 476000
= 80/100 × 476000
= 38080000/100
= 380800
B)
Answer: B
Question: Find the value of (875 233/899) × 899
Options:
A)786500
B)786528
C)786652
D)786700
E)786858
Rationale: (875 233/899) × 899
(786625 + 233)/899 × 899
786858/899 × 899
786858
E
Answer: E
Question: x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal
Options:
A)33
B)36
C)44
D)63
E)66
Rationale: From the given equations, a = 4x, b = 4z
(10a+b) - (10x+z) = 40x+4z - 10x-z = 30x +3z = 3(10x+z)
Therefore the resultant should be divisible by 3 which isn't possible only in the case of C.
Hence C is the answer
Answer: C
Question: If a wholesaler distributes items to several outlets (A, B, C and D) in the ratio of 1/12 : 1/13 : 1/15 : 1/2, then find the total number of items the wholesaler distributes?
Options:
A)567
B)167
C)267
D)467
E)667
Rationale: Here, A : B : C : D = 1/12 : 1/13 : 1/15 : 1/2
1) L.C.M of 12 : 13 : 15 : 2 is 780
2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/12) x 780 = 65
B = (1/13) x 780 = 60
C = (1/15) x 780 = 52
D = (1/2) x 780 = 390
3) Total number of toys = (65 x + 60 x + 52 x + 390 x) = 567 x
Minimum number of pens (x) = 1
Therefore, total number of items = 567 items.
Correct option :A
Answer: A
Question: Rs.560 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?
Options:
A)Rs.142.37
B)Rs.152.37
C)Rs.242.37
D)Rs.210
E)Rs.142
Rationale: A+B+C = 560
5A = 6B = 8C = x
A:B:C = 1/5:1/6:1/8
= 24:20:15
15/59 * 560 = Rs.142.37
ANSWER:A
Answer: A
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 65
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
Options:
A)51
B)88
C)90
D)103
E)162
Rationale: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 65 + (35-15) + (40-10-12) = 65+20+18 = 103
Hence, Answer will be D.
Answer: D
Question: Find the odd man out. 3, 5, 15, 75, 1120, 84375
Options:
A)15,
B)84375
C)1120
D)75
E)3
Rationale: 3
5
3 × 5 = 15
5 × 15 = 75
15 × 75 = 1125
75 × 1125 = 84375
Hence, 1120 is wrong. 1125 should have come in place of 1120
Answer is C
Answer: C
Question: When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 6. How many values less than 100 can n take?
Options:
A) 0
B) 2
C) 3
D)6
E) 5
Rationale: a quick approac to this Q is..
the equation we can form is.. 3x+2=7y+5..
3x-3=7y... 3(x-1)=7y...
so (x-1) has to be a multiple of 7 as y then will take values of multiple of 3..
here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached
as (29-1)*3=84 and next multiple of 7 will be 84+21>100..
ans 6.. D
Answer: D
Question: A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one–fifth of the average o fthe two areas. What is the area of the smaller part in hectares?
Options:
A)225
B)280
C)300
D)385
E)None
Rationale: Solution
Let the areas of the two parts be
x and (700 - x)hectares	= [x - (700 - x)]
= 1 / 5 x [x + (700 - x)/ 2]
= 2x - 700= 70
x = 385.
Answer D
Answer: D
Question: In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 19th board counting from the bottom of the stack. How many boards are in the stack?
Options:
A)37
B)36
C)35
D)34
E)32
Rationale: Counting from the top, after the 20th board, there are 17 boards left to count.
The answer is A.
Answer: A
Question: A man counted his animals, 80 heads and 270 legs (ducks and goats). how many goats are there?
Options:
A)30
B)40
C)50
D)60
E)55
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=270 and divide 2d+4g=270 by 2 we get d+2g=135 -----------> eq2
subtract eq1 from eq2
we get no of goats=55
ANSWER:E
Answer: E
Question: A tourist purchased a total of $4,500 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
Options:
A)$1,430
B)$2,310
C)$3,290
D)$4,270
E)$5,150
Rationale: Let the number of $10 checks cashed beT
Let the number of $50 checks cashed beF
7 checks cashed;
T+F=7
Now; T can be F+1 OR T can be F-1
Let's check both conditions;
T=F+1
T+F=7
F+1+F=7
2F=6
F=3
T=4
Value cashed = 3*50+4*10=150+40=$190
Let's check the other condition as well;
T=F-1
T+F=7
F-1+F=7
2F=8
F=4
T=3
Value cashed = 4*50+3*10=200+30=$230
The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.
Value cashed = $230
Value lost = 4500-230 = $4270
Ans:D
Answer: D
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 0: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
Options:
A)4: 45 p.m.
B)2: 20 p.m.
C)5: 20 p.m.
D)5: 35 p.m.
E)6: 00 p.m.
Rationale: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 0:20 +2=2:20
Hence answer is B.Hope i am correct
Answer: B
Question: A string of length 40 metres is divided into three parts of different lengths. The first part is three times the second part, and the last part is 23 metres smaller than the first part.
Find the length of the largest part.
Options:
A)27
B)4
C)5
D)9
E)8
Rationale: Explanation :
Let the 2nd piece length be x.
1st piece length is 3x.
3rd piece length is 3x – 23.
Sum of all the pieces is 40.
3x + x + 3x – 23 = 40.
7x = 63.
x = 9.
Lengths of the pieces are 27, 9, 4.
Answer : A
Answer: A
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?
Options:
A)22
B)88
C)12
D)77
E)87
Rationale: S.I. for 3 years = (12005 - 9800) = Rs. 2205
S.I. for 5 years = Rs. 2205/3 * 5 = Rs. 3675.
Principal = (9800 - 3675) = Rs. 6125
Hence, rate = (100 * 3675) / (6125 * 5) = 12%
Answer: C
Answer: C
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
Options:
A)20:15:16
B)20:15:18
C)20:15:12
D)20:15:11
E)20:15:13
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: C
Question: A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 oranges are used, how many lemons are needed?
Options:
A)50
B)100
C)200
D)400
E)700
Rationale: 10%= 200 fruit
100%=2000 fruit
20% of 2000 fruit=400 fruit
400 lemons
ANSWER:D
Answer: D
Question: An article is bought for Rs.500 and sold for Rs.400, find the loss percent?
Options:
A)18 2/3%
B)16 7/3%
C)20%
D)16 2/3%
E)76 2/3%
Rationale: 500 ---- 100
100 ---- ? => 20%
Answer:C
Answer: C
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
Options:
A)2(5/11)days
B)3(5/11)days
C)4(5/11)days
D)6(5/11)days
E)8(5/11)days
Rationale: B
3(5/11)days
A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 2 days.
The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
Answer: B
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
Options:
A)8 min
B)7 min
C)5 min
D)9 min
E)4 min
Rationale: 1/10 + 1/15 - 1/x
= 1/18
x = 9
Answer: D
Answer: D
Question: Ravi and Kavi start a business by investing â‚¹ 2000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
Options:
A)2 : 36
B)5 : 36
C)7 : 36
D)1 : 36
E)3 : 36
Rationale: Ratio of profit = Ratio of investments
= 2000 : 72000 = 1 : 36
Answer : D
Answer: D
Question: On the average Mr.Jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed.How much hours should jackson and assistant has t plan for 30 min meeting?
Options:
A)4.5 hr
B)4.8 hr
C)4.9 hr
D)5.5 hr
E)6.5 hr
Rationale: for a 1 hour talk he took total of 9 hr time
1hr=9hr(2+7)
30 min=1/2hr =?
so 9*1/2 div by 1
4.5 hr
ANSWER:A
Answer: A
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 30 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
Options:
A)a. 43
B)b. 45
C)c. 55
D)d. 68
E)e. 60
Rationale: 30 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (30 * 12.5 * 100) / (2.5 * 200)
thus, X = 75
Thus, more men needed to finish the task = 75-30=45
hence Answer is B
Answer: B
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 180, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
Options:
A)31
B)33
C)55
D)77
E)88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 180 => .1x + 3/4x = 180 => x = 211
211 - 180 = pure gala = 31.
A
Answer: A
Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 3/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
A)63/280
B)1/280
C)3/56
D)3/35
E)7/40
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*4/7 + 1/5*5/8*3/7 + 4/5*3/8*3/7 = 63/280.
Answer: A
Answer: A
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
Options:
A)7
B)6
C)2
D)8
E)4
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B
Answer: B
Question: A sum of money at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is :
Options:
A)400
B)500
C)600
D)700
E)800
Rationale: SI of 5 year = (1020-720)=300
so, SI of 1 year=300/5=60
so, SI of 2 year=60*2=120
so, sum is =(720-120)=600
ANSWER:C
Answer: C
Question: Jack and Jill are marathon runners. Jack can finish a marathon (43 km) in 4.5 hours and Jill can run a marathon in 4.3 hours.What is the ratio of their average running speed? (Jack: Jill)
Options:
A)14/15
B)43/45
C)4/5
D)5/4
E)Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 43 /(9/2) = 86/9
Average Speed of Jill = 43/(4.2) = 10
Ratio of Average speed of Jack to Jill = (86/9)/10 = 86/90 = 43/45
Answer B
Answer: B
Question: The owner of a furniture shop charges his customer 10% more than the cost price. If a customer paid Rs. 7350 for a computer table, then what was the cost price of the computer table?
Options:
A)Rs.6289
B)Rs.6298
C)Rs.6681
D)Rs.6725
E)Rs.6708
Rationale: CP = SP * (100/(100 + profit%))
= 7350(100/110) = Rs.6681.
Answer: C
Answer: C
Question: Find the number of zero’s in 173! (173 Factorial)?
Options:
A)38
B)39
C)40
D)41
E)42
Rationale: no of zeroes in 173! is
173/5=34(quotient)
34/5=6(quotient)
6/5=1(quotient)
34+6+1=41
ans 41 zeroes
ANSWER:D
Answer: D
Question: A small water pump would take 4 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
Options:
A)1/6
B)4/9
C)1/4
D)5/9
E)1/3
Rationale: Rate of the small pump is 1/4 tank/hour
Rate of the larger pump is 1/(1/2) or 2 tank/hour;
Combined rate of the two pumps is 1/4+2=9/4 tank/hour, together they will fill the empty tank in 1/(9/4)) = 4/9 hours (time=job/rate).
Answer: B
Answer: B
Question: When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 71.2 , what is the value of n?
Options:
A)9
B)20
C)55
D)70
E)80
Rationale: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:
We're told that K and N are both INTEGERS.
Since K/N = 81.2, we can say that K = 81.2(N)
N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.
With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)
Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH
Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.
Final Answer:
E
Answer: E
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 8.
Options:
A)161
B)152
C)154
D)158
E)144
Rationale: D = d * Q + R
D = 17 * 9 + 8
D = 153 + 8
D = 161
ANSWER A
Answer: A
Question: Find the product of the localvalue and absolutevalue of 6 in 20618?
Options:
A)6300
B)1100
C)1200
D)1300
E)3600
Rationale: Local value of 6 = 6 x 100 = 600
Place value of 6 = 6
There fore = 6 x 600 = 3600
E
Answer: E
Question: If the day before yesterday was Wednesday, what day will be the day after tomorrow?
Options:
A)Sunday
B)Monday
C)Tuesday
D)Friday
E)Saturday
Rationale: Explanation:
Day before yesterday was Wednesday
=>Yesterday was a Thursday
=>Today is a Friday
=>Tomorrow is a Saturday
=>The day after tomorrow will be a Sunday
Answer: Option A
Answer: A
Question: If x, y, and z are positive integers, and 3x = 5y = 6z, then the least possible value of x + y + z is
Options:
A)21
B)28
C)37
D)42
E)60
Rationale: Take LCM of 3,5 and 6 = 30
Now 3x = 30 => x =10
5y = 30 => y = 6
6z = 30 => z =5
10+6+5 = 21.
Option A.
Answer: A
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Options:
A)10/21
B)1/21
C)9/11
D)7/11
E)6/11
Rationale: Total number of balls = 2 + 3 + 2 = 7
n(S) =Total number of ways 7 = 7C2
let E = event of drawing 2 balls, none of them is blue
n(E) = no of ways of drawing 2 balls, none of them is blue
=No of ways of drawing 2 balls from the total= 5C2
5*4/7*6 = 10/21
ANSWER A
Answer: A
Question: Out of 10 students in a class, 4 are from Maharashtra, 3 are from Karnataka, and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
Options:
A)1/3
B)4/9
C)5/6
D)3/7
E)1/4
Rationale: Total possible ways of selecting 4students out of 10= 10C4 = (10*9*8*7)/(4*3*2*1) =210
The number of ways of selecting a 4 students in which no student belongs to Karnataka = 7C4
Number of ways of selecting atleast one student from Karnataka = 15C4-7C4 = 175
Probability = 175/210 = 5/6
Answer is C
Answer: C
Question: The product of face value of 3 and local value of 6 in the numeral 78934064 is
Options:
A)18
B)24
C)180
D)240
E)108
Rationale: (Face value of 3) x (Local value of 6) = (3 x 60) = 180
C
Answer: C
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)2882
C)2799
D)2778
E)2901
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: A
Question: Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
A)3/140
B)1/28
C)7/40
D)3/35
E)5/40
Rationale: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*5/7 + 1/5*5/8*2/7 + 4/5*3/8*2/7 = 7/40.
Answer: C.
Answer: C
Question: A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability T that a + b is prime?
Options:
A) 0
B) 1/12
C) 5/12
D) 7/18
E) 4/9
Rationale: Total # of outcomes is 6*6=36;
Favorable outcomes:
a-b --> prime
1-1 --> 2;
1-2 --> 3;
2-1 --> 3;
1-4 --> 5;
4-1 --> 5;
2-3 --> 5;
3-2 --> 5;
1-6 --> 7;
6-1 --> 7;
2-5 --> 7;
5-2 --> 7;
3-4 --> 7;
4-3 --> 7;
6-5 --> 11;
5-6 --> 11.
Total of 15 favorable outcomes
T=15/36.
Answer: C.
Answer: C