divelab/Sys2Bench huggingface dataset:
Question: Ayesha's father was 35 years of age when she was born while her mother was 31 years old when her brother four 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)8 years
E)9 years
Rationale: Mother's age when Ayesha's brother was born = 31 years.
Father's age when Ayesha's brother was born = (35 + 4) years = 39 years.
Required difference = (39 - 31) years = 8 years. Answer: Option D
Answer: D
Question: In a certain village, 150 litres of water are required per household per month. At this rate, if there are 10 households in the village, how long (in months) will 6000 litres of water last?
Options:
A)8
B)10
C)6
D)2
E)4
Rationale: I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p:
In a certain village,m 150 litres of water are required per household per month. At this rate, if there aren 10 households in the village, how long (in months) willp2000litres of water last?
Water required is 150*10=1500 (m*n)
Water available is 6000 (p)
It will last 4 months (p/m*n)
Ans :E
Answer: E
Question: Three persons are walking from a place A to another place B. Their speeds are in the ratio of 4 : 3 : 5. The time ratio to reach B by these
persons will be :
Options:
A)4 : 3 : 5
B)15 : 20 : 12
C)5 : 3 : 4
D)20: 15 : 12
E)None
Rationale: Sol.
Ratio of speeds = 4 : 3 : 5
∴ Ratio of times taken = 1/4 : 1/3 : 1/5 = 15 : 20 : 12
Answer B
Answer: B
Question: In how many different ways can the letters of the word 'BANKING' be arranged so that the vowels always come together ?
Options:
A)740
B)720
C)800
D)550
E)690
Rationale: In the word 'BANKING', we treat the two vowels AI as one letter. Thus,we have BNKNG (AI)
This has 6 letters of which N occurs 2 times and the rest are different.
Number of ways of arranging these letters= 6!/(2!)(1!)(1!)(1!)(1!)=360.
Now 2 vowels AI can be arranged in 2!=2 ways.
Required number of ways =(360*2)=720.
Answer is B
Answer: B
Question: What is the units digit of the expression 14^7−17^4?
Options:
A) 0
B) 3
C) 4
D) 8
E) 6
Rationale: I think answer on this one should be D too. Since we know that 14^7>17^4, as Will said one should always check if the number is positive.
Answer: D
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 70 minutes. When both pipes are opened, find when the cistern will be full?
Options:
A)17 minutes
B)87 minutes
C)70 minutes
D)28 minutes
E)11 minutes
Rationale: 1/20 - 1/70 = 1/28
28 minutes
Answer:D
Answer: D
Question: Convert 700 miles into meters?
Options:
A)784596
B)1126538
C)804670
D)784596
E)864520
Rationale: 1 mile = 1609.34 meters
700mile = 700*1609.34 = 1126538 meters
Answer is B
Answer: B
Question: If point A coordinates are (-5, -3) point B coordinates are (8 ,4 ) if C is along the line A-B so that AC = 1/2 CB. What are the coordinates of point C.
Options:
A)(-2, - 2/3)
B)(2, -2/3)
C)(2/3, -2)
D)(0, 2)
E)(2, 2/3)
Rationale: Look at the diagram below:
Line segment.pngSince, AC= 1/2 CB, then AC = 1/3 AB. This implies that point C is closer to A than to B, which on the other hand implies that the x-coordinate of C must be less than (-5+8)/2=0.5. Only D and A fits, but as (0 , 2) is clearly not on line segment AB, then the answer must be E.
Answer: E.
Answer: E
Question: If it is 8:27 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.)
Options:
A)8:22
B)8:24
C)8:27
D)8:31
E)8:30
Rationale: 8:27minus 2,880,717in any way must end with 0, the only answer choice which ends with 0 is E.
Answer: E.
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 7 seconds. Find the length of the train.
Options:
A)116.67
B)882
C)772
D)252
E)121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 7 = 116.67 meter.Answer: A
Answer: A
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)8 min
B)24 min
C)12 min
D)6 min
E)4 min
Rationale: Explanation:
S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
E)
Answer: E
Question: The average of 35 numbers is 25. If each number is multiplied by 5, find the new average?
Options:
A)125
B)66
C)77
D)16
E)188
Rationale: Sum of the 35 numbers = 35 * 25 = 875
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5 = 125.
Answer: A
Answer: A
Question: An employer has 4 applicants for a programming position and 4 applicants for a manager position. If the employer must hire 3 programmers and 2 managers, what is the total number of ways the employer can make the selection?
Options:
A)a) 1,490
B)b) 132
C)c) 120
D)d) 60
E)e) 23
Rationale: 4C3 * 4C2 = 24. Answer C.
Answer: C
Question: A clock is set right at 12 noon on Monday. It losses 1/2% on the correct time in the first week but gains 1/4 on the true time during the second week. The time shown on Monday after two weeks will be
Options:
A)12:25:12
B)11:34:48
C)12:50:24
D)12:24:16
E)None of these
Rationale: Solution: Time lost over two weeks = 25% a week time(given that 1/2% clock loses in first week and in the second week it gains 1/4% on true time)
A week = 168 hours
Hence, clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds.
Thus, correct time = 12:25:12.
Answer: Option A
Answer: A
Question: Two employees Y and Z are paid a total of Rs. 550 per week by their employer. If Y is paid 120 percent of the sum paid to Z, how much is Z paid per week?
Options:
A)A)Rs.200
B)B)Rs.220
C)C)Rs.250
D)D)Rs.300
E)E)Rs.350
Rationale: Let the amount paid to Y per week = y
and the amount paid to Z per week = z
Then x + y = 550
But y = 120% of z = 120z/100 = 12z/10
∴12z/10 + z = 550
⇒ z[12/10 + 1] = 550
⇒ 22z/10 = 550
⇒ 22z = 5500
⇒ z = 5500/22 = 500/2 = Rs.250
C
Answer: C
Question: Townville has 100 residents, and 20 of them are females. If half of Townville’s male residents are smokers, and 1/4 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
Options:
A)50
B)60
C)55
D)65
E)70
Rationale: Number of people =100
Females = 20
men = 100-20=80
Half of the men are smoker80/2=40, that means the remaining men 80-40=40 are non smokers.
1/4 females are smoker. i.e 1/4*20 = 5.
20-5=15 females are non smokers
So, total number of non smokers in the town are 40+15 =55
Answer : C
Answer: C
Question: Emma worked for h hours each day for d consecutive days. If she earns $4.50 per hour, what is the total amount she earned?
Options:
A)4.50/d + h
B)4.50 + d + h
C)4.50 + dh
D)4.50h + d
E)4.50dh
Rationale: H hours for d days.
Income each day = 4.5*h
Total income = 4.5*h*d
Correct option: E
Answer: E
Question: A clock is set at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?
Options:
A)38
B)11
C)237
D)29
E)112
Rationale: Time from 5 a.m. on a day to 10 p.m. on 4th day = 89 hours.
The faulty clock shows only 1424 min for 24 hours in correct clock.
So 1 minute of the faulty clock = 24/1424 hours
1 hour of the faulty clock = 24/1424 × 60 hours
89 hours of the faulty clock = 24/1424 × 60 × 89 = 90 hours.
So true time is 1 hour more than 10 pm. i.e., 11 pm.AnswerB
Answer: B
Question: Of the 100 people in a room, 2/5 are women. If 1/4 of the people are married, what is the maximum number of women in the room who could be unmarried?
Options:
A)32
B)34
C)36
D)38
E)40
Rationale: women = 2/5 * 100 = 40
married = 1/4 * 100 = 25
unmarried = 75
max(un-married women) = 40
Answer E
Answer: E
Question: In Sam's hanger there are 22 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
Options:
A)1.
B)2.
C)3.
D)4.
E)5.
Rationale: Total boxes = 22
Filled with toys = 16
Filled with appliance = 6
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 6 - 3 = 3
Correct Option: C
Answer: C
Question: When tossed, a certain six-sided die has an equal probability of landing on any of the six sides. If the die is tossed 4 times, what is the probability that it will land on the same side each time?
Options:
A)1/12
B)1/18
C)1/36
D)1/216
E)1/1296
Rationale: On the first toss, the die will land on one of the sides.
On the second toss, the probability of landing on the same side is 1/6.
On the third toss, the probability of landing on the same side is 1/6.
On the fourth toss, the probability of landing on the same side is 1/6.
P(same side four times)=1/6*1/6*1/6=1/216.
The answer is D.
Answer: D
Question: There are 16 bees in the hive , then 6 more fly. How many bees are there in all?
Options:
A)7
B)33
C)22
D)17
E)25
Rationale: 16+6=22 . Answer is C.
Answer: C
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.4 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
Options:
A)24 years
B)44 years
C)32 years
D)64 years
E)84 years
Rationale: 32 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 4 = 11
4A + 4 = 9
9(5A + 4)=11(4A + 4)
A = 8
Thomasâ€™s current age = 4A
= 32 years.
C
Answer: C
Question: Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in four hours, what fraction of the room can Joseph paint in 20 minutes?
Options:
A)1/4x
B)x/(x-12)
C)(x-4)/12x
D)x/(x-4)
E)(x-4)/x
Rationale: Let J be Joseph's rate per hour.
1/x + J = 1/4 of a room per hour
J = 1/4 - 1/x, of a room per hour
In 20 minutes, Joseph can paint 1/3*(1/4-1/x) = 1/12-1/3x = (x-4)/12x
The answer is C.
Answer: C
Question: The ratio of two quantities is incorrect when written as 10 to 14. How should this ratio be written?
Options:
A)5:14
B)10:7
C)20:24
D)5:7
E)It cannot be determined from the information given
Rationale: A ratio should be reduced to the lowest common denominator.
10:14 means 10x:14x which can be written as 5(2):7(2)...
ANSWER:D
Answer: D
Question: If the annual increase in the population of a town is 10% and the present number of people is 13000, what will the population be in 2 years?
Options:
A)15730
B)15240
C)12456
D)11452
E)10002
Rationale: The required population is = 13000 (1 + 10/100)^2
= 13000 * 11/10 * 11/10
= 15730
Answer is A
Answer: A
Question: The difference between the simple interest on a certain sum at the rate off 10% per annum for 2 years and compound interest which is compounded every 6 months is Rs. 124.05. What is the principal sum?
Options:
A)Rs. 6000
B)Rs. 8000
C)Rs. 12000
D)Rs. 10000
E)Rs. 5000
Rationale: Explanation:
Let the sum be P
Compound Interest on P at 10% for 2 years when interest is compounded half-yearly
=P(1+(R/2)/100)2T − P = P(1+(10/2)/100)2×2 − P = P(1+1/20)4 − P = P(21/20)4 − P
Simple Interest on P at 10% for 2 years = PRT/100 = (P × 10 × 2)/100 = P/5
Given that difference between compound interest and simple interest = 124.05
=> P(21/20)4 − P − P/5 = 124.05
=> P[(21/20)4 − 1 − 15] = 124.05
=> P[(194481 − 160000 − 32000)/160000] = 124.05
=> P[2481/160000] = 124.05
=> P = (124.05 × 160000)/2481 = 160000/20 = 8000
Answer: Option B
Answer: B
Question: Three people (1 couple and 1 single) are seated at random in a row of 4 chairs. What is the probability that the couple does not sit together?
Options:
A)3/7
B)1/2
C)2/5
D)3/4
E)5/12
Rationale: The total number of arrangements of 3 people is 4*3*2 = 24
Let's think of the couple as a single unit.
The number of arrangements when the couple sits together is 3*2*2 = 12.
Note that we multiply by 2 because the couple can switch places with each other.
The number of ways the couple won't sit together is 24 - 12 = 12
P(couple won't sit together) = 12/24 = 1/2
The answer is B.
Answer: B
Question: 33 1/3% of 36?
Options:
A)16
B)21
C)18
D)12 number
E)18
Rationale: Explanation:
33 1/3 % = 1/3
1/3 * 36 = 12
Answer: Option D
Answer: D
Question: The number of new words that can be formed by rearranging the letters of the word 'FACEUP' is ?
Options:
A)720
B)719
C)220
D)178
E)266
Rationale: Number of words which can be formed = 6! - 1
= 720 - 1
=719.
Answer:B
Answer: B
Question: Subtracting 30 from a number, the remainder is one fourth of the number. Find the number?
Options:
A)29
B)88
C)40
D)28
E)27
Rationale: Explanation:
3/4 x = 30 => x = 40
Answer:C
Answer: C
Question: 6 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?
Options:
A)4
B)6
C)16
D)120
E)256
Rationale: it is like a circular arrangement.
total ways for n people to arrange in a circle is = factorial (n-1)
in this case n= 6
hence ans = 5 factorial = 120
hence D
Answer: D
Question: In the first hour of a two-hour trip, a car traveled 2d kilometers, and in the second hour of the trip, the car traveled one-half that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
Options:
A) d
B) 1/3*d
C) 1/2*d
D) 3/4*d
E) 3/2*d
Rationale: Solution:
Lets look at the information given in the question...
Total time travelled = 2 hrs
Distance travelled first hour = 2d
Distance travelled second hour = d
The question is asking for the avg speed at which the car travels for 2 hrs
We know that avg speed = total distance/total time
Lets place the information given in the question to the formula above = (2d+d)/2
= 3/2*d
We find that option E is the answer as it gives the same expression as found in our calculation above. Answer option E
Answer: E
Question: In a apartment, 40% of the people speak English, 40% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
Options:
A)1/2
B)2/3
C)2/5
D)2/7
E)2/9
Rationale: P (E) = 40 / 100 = 4 / 10 , P (H) = 40 / 100 = 4 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (4 / 10) + (4 / 10) - (3 / 10) = 4 / 10 = 1/2
A
Answer: A
Question: Magna Bulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magna Bulk charges m dollars for each crate?
Options:
A)100bd/m
B)100m/(bd)
C)bd/(100m)
D)m/(bd)
E)bd/m
Rationale: crate has = bd magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = 100 m / bd
Answer: B
Answer: B
Question: 45 workers work 8 hours to dig a hole 30 meters deep. How many extra workers should be hired to dig another hole 40 meters deep by working for 6 hours?
Options:
A)75
B)80
C)50
D)35
E)40
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 40
x = 80 total workers
80 - 45 = 35
The answer is D.
Answer: D
Question: About the number of pairs which have 12 as their HCF and 136 as their LCM, the conclusion can be
Options:
A)no pair exist
B)only two such pairs exist
C)many such pairs exist
D)only one such pair exists
E)None of these
Rationale: Explanation:
HCF is always a factor of LCM. ie., HCF always divides LCM perfectly.
Correct Option: A
Answer: A
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
Options:
A)49 m2
B)50 m2
C)52 m2
D)53.5 m2
E)55 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
= 49 m2.
answer :A
Answer: A
Question: 11 persons are sitting ina row. how many ways can 11persons be arranged in a row such that 3 persons should always be together?
Options:
A)7!×3!
B)7!×2!
C)9!×3!
D)7!×1!
E)6!×2!
Rationale: Given that three particular persons should always be together. Hence, just group these three persons together and consider as a single person.
Therefore we can take total number of persons as 9. These 9 persons can be arranged in 9! ways.
We had grouped three persons together. These three persons can be arranged among themselves in 3! ways.
Hence, required number of ways
=9!×3!
C
Answer: C
Question: A man can row upstream at 29km/hr and down stream at 15km/hr find mans rate of the current ?
Options:
A)9.8km/hr
B)3.6km/hr
C)8.9km/hr
D)7km/hr
E)5.9km/hr
Rationale: given upstream(u) =29km/hr
down stream (v)= 15km/hr rate of the current =1/2(u-v) =1/2(29-15)=7km/hr
Answer is (D)
Answer: D
Question: If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
Options:
A)2
B)5
C)6
D)8
E)None of these
Rationale: Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
P = 1.
Option E
Answer: E
Question: It being given that √ 15 = 3.88, the best approximation to √5/3 is
Options:
A)0.43
B)1.89
C)1.29
D)1.63
E)1.54
Rationale: x = √(5/3) = √(5*3)/(3*3)
= √15 /√ 9
= √15/3
= 3.88/3 = 1.29
Answer is C.
Answer: C
Question: The numbers of pizza slices that are sold in Joey's Pizza are only in quantities of 4 and 9 slices per customer. How many slices cannot be bought?
Options:
A)58.
B)50.
C)67.
D)74.
E)22.
Rationale: Answer:	Let X pizzas of 4 slices and Y pizzas of 9 slices.
4X + 9Y.
Lets check options wise.
A. 58 => 4(19) + 6(32)
B. 50 => we can't write anything with 4 and 6 series..Lets try 4(1) + 9(5) = 49 , 4(6) + 9(3) = 51 , nothing works out
C. 67 => 4(10) + 9(3)
D. 74 => 4(5) + 9(6)B. 74 => 4(5) + 9(6)
E. 22 => 4(1) + 9(2)
Answer: correct option is B
Answer: B
Question: What annual payment will discharge a debt of Rs. 1050 due in 2 years at the rate of 5% compound interest?
Options:
A)993.2
B)551.25
C)534.33
D)543.33
E)564.69
Rationale: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1050
820x + 1050 * 441
x = 564.69
So, value of each installment = Rs. 564.69
Answer: Option E
Answer: E
Question: A group of candidates for two analyst positions consists of six people. If one-third of the candidates are disqualified and three new candidates are recruited to replace them, the number of ways in which the two job offers can be allocated will:
Options:
A)Drop by 40%
B)Remain unchanged
C)Increase by 20%
D)Increase by 40%
E)Increase by 60%
Rationale: Initially 6 people for 2 positions, meaning
6 - 1st position
5 - 2nd position
Total combinations- 5*6 = 30
Now 1/3rd not qualified, so reduce by 2. Hence, now we have 4+3 candidates for the position.
Same as above, 7*6 for two positions will give 42 combinations. Thus, 42-30/30 = 40% increase;
ANSWER:D
Answer: D
Question: Two numbers X and Y are such that the sum of 5% of X and 4% of Y is two-third of the sum of 6% of X and 8% of Y. Find the ratio of X : Y.
Options:
A)4:3
B)3:2
C)1:2
D)2:1
E)3:5
Rationale: 5% of X + 4% B = 2/3 (6% X + 8% Y)
= 5/100X+4/100Y = 2/3(6/100 X + 8/100 Y)
1/100X = 1/75 Y
X/Y = 100/75 = 4/3
Ratio 4:3
ANSWER A
Answer: A
Question: The ratio of red, yellow, and green jelly beans in a jar is 1:2:3. If the number of jelly beans is increased by 10%, 20%, and 30% respectively, what will be the new ratio?
Options:
A)11:24:39
B)7:19:35
C)6:18:29
D)4:15:28
E)2:11:25
Rationale: The new ratio will be 1.1:2.4:3.9=11:24:39.
The answer is A.
Answer: A
Question: If x is the sum of s and t, then which one of the following must equal s – t ?
Options:
A)x-2t
B)x+2t
C)x-t
D)x+t
E)x/2t
Rationale: Given x= s+t if you subtracts both side with -2t
x-2t = s-t
Answer : A
Answer: A
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in two times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 30 minutes, then how many minutes does it take pump X alone to fill the tank?
Options:
A)15
B)16
C)18
D)20
E)24
Rationale: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/30 per minute.
(R - V/30)*2T=V=RT.
(R-V/30)*2=R
R=V/15.
It takes pump X 15 minutes to fill the tank.
The answer is A.
Answer: A
Question: The length of each side of square A is increased by 100 percent to make square B. If the length of the side of square B is increased by 60 percent to make square C, by what percent is the area of square C greater than the sum of the areas of squares A and B?
Options:
A)75%
B)80%
C)104.8%
D)150.5%
E)180%
Rationale: Let length of each side of square A be 10
Area of A = 10^2 = 100
Since , length of each side of square A is increased by 100 percent to make square B
length of each side of square B = 2*10 = 20
Area of B = 20^2 = 400
Since , length of the side of square B is increased by 60 percent to make square C
length of each side of square C= 1.6*20 = 32
Area of C= 32^2 = 1024
Difference in areas of C and cummulative areas of A and B = 1024 -(400+100) = 524
percent is the area of square C greater than the sum of the areas of squares A and B = (524/500) * 100 % = 104.8%
Answer C
Answer: C
Question: Sum of two numbers is 35. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
Options:
A)A)5
B)B)9
C)C)11
D)D)22
E)E)15
Rationale: Explanation:
x + y = 35
2x – 3y = 5
x = 22 y = 13
D)
Answer: D
Question: What is the sum of all four digit integers formed using the digits 2, 3, 4 and 5 (repetition is allowed)
Options:
A)444440
B)610000
C)666640
D)995456
E)880000
Rationale: n = 4 * 4 * 4 * 4 = 256
<x> = (5555+ 2222) / 2 = 3888.5
Sum = number of integers x average value
n * <x> = 256 * 3888.5 = 711040
answer = D
Answer: D
Question: A committee of three people is to be chosen from 3 married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
Options:
A)16
B)24
C)26
D)30
E)8
Rationale: Total no of ways of choosing a committee = 6C3 = 20
No of ways to choose first couple = 3C1 = 3
No of ways to choose 1 person from remaining 4 = 4C1 = 4
Total number of ways of choosing a married couple to be in the same committee = 3*4=12
So, no of ways not choosing a married couple = 20-12 =8
ANS:E. 8
Answer: E
Question: After depositing a check into his checking account, the amount of money in Daniel's checking account increased from $9,090.00 to $9180.90. What was the percentage of the increase?
Options:
A)2%
B)1.5%
C)1%
D)0.5%
E)None
Rationale: First we need to figure out how much money Daniel deposited:
=$9180.90-$9,090.00=$90.90
Now we need to determine what percentage $90.90 is of $9,090.00:
90.9/9090*100 =1%
answer is C.
Answer: C
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
Options:
A)22
B)12
C)98
D)27
E)14
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
Answer: B
Answer: B
Question: 100 identical coins each with probability 'pp' showing up heads & tossed. If 0<p<10<p<1 and the probability of heads showing on 50 coins is equal to that ofheads on 51 coins, then the value of pp is?
Options:
A)50/101
B)51/103
C)51/101
D)63/111
E)63/113
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: C
Question: The greatest number of four digits which is divisible by 20,25,30 and 70 is:
Options:
A)8400
B)9200
C)9600
D)9800
E)9960
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 20, 25, 30 and 70 is 2100.
On dividing 9999 by 2100, the remainder is 1599.
Required number (9999 - 1599) = 8400.
Answer: Option A
Answer: A