divelab/Sys2Bench huggingface dataset:
Question: The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$430 per month. The salary of the new supervisor is:
Options:
A)870
B)600
C)287
D)771
E)191
Rationale: Explanation:
Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870
Now total salary of 8 workers = 3870 âˆ’ 870 = 3000
Total salary of 9 workers including the new supervisor = 9 Ã— 430 = 3870
Salary of the new supervisor = 3870 âˆ’ 3000 = 870
Answer: A
Answer: A
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
Options:
A)2.91 m
B)3 m
C)5.82 m
D)4.32 m
E)None of these
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
Answer: Option B
Answer: B
Question: Lionel left his house and walked towards Walt's house, 48 miles away. Two hours later, Walt left his house and ran towards Lionel's house. If Lionel's speed was 3 miles per hour and Walt's 4 miles per hour, how many miles had Lionel walked when he met Walt?
Options:
A)12
B)16
C)20
D)24
E)28
Rationale: In the first 2 hours Lionel at the rate of 3 miles per hour covered distance=rate*time=3*2=6 miles. So, the distance between him and Walt was 48-6=42 miles when Walt left his house. Now, their combined rate to cover this distance was 3+4=7 miles per hour, hence they will meet (they will cover that distance) in time=distance/rate=42/7=6 hours. Total time that Lionel was walking is 2+6=8 hours, which means that he covered in that time interval distance=rate*time=3*8=24 miles.
Answer: D.
Answer: D
Question: The average weight of 5 person's increases by 4 kg when a new person comes in place of one of them weighing 50kg. What is the weight of the new person?
Options:
A)70
B)86.5
C)80
D)88.5
E)75
Rationale: Total increase in weight =5 × 4=20
If x is the weight of the new person, total increase in weight = x−50
=> 20= x - 50
=> x = 20+50= 70
ANSWER:A
Answer: A
Question: The least perfect square, which is divisible by each of 21,36 and 66 is
Options:
A)213444
B)214344
C)214434
D)213443
E)None of these
Rationale: L.C.M. of 21, 36, 66 = 2772.
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 22 x 32 x 72 x 112 = 213444
Answer A
Answer: A
Question: X, Y and Z contract a work for Rs. 1100. X and Y together are to do 7/11 of the work. C’s share is:
Options:
A)Rs.366.6
B)Rs.400
C)Rs.600
D)Rs.800
E)Rs.900
Rationale: (A + B) : C = 7/11 : 4/11 = 7 : 4.
Therefore, C’s share = Rs. 1100 * 4/11
= Rs.400.
ANSWER:B
Answer: B
Question: What is the units digit of 63^3 * 17^3 * 49^3?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: The units digit of 63^3 is the units digit of 3*3*3 = 27 which is 7.
The units digit of 17^3 is the units digit of 7*7*7 = 343 which is 3.
The units digit of 49^3 is the units digit of 9*9*9 = 729 which is 9.
The units digit of 7*3*9 = 189 is 9.
The answer is E.
Answer: E
Question: What is the present worth of Rs. 176 due in 2 years at 5% simple interest per annum?
Options:
A)288
B)160
C)120
D)277
E)6123
Rationale: Let the present worth be Rs. x. Then,
S.I. = (176 - x)
(x * 5 * 2) / 100 = (176 - x)
10x = 17600 - 100x
110x = 17600 => x = 160.
Answer: B
Answer: B
Question: If log 27 = 1.431, then the value of log 9 is:0.934
B.	0.945
C.	0.954
D.	0.958
Options:
A)0.934
B)0.945
C)0.954
D)0.958
E)0.964
Rationale: log 27 = 1.431
log (3^3 ) = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(3^2 ) = 2 log 3 = (2 x 0.477) = 0.954.
Answer is C.
Answer: C
Question: There are 28 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
Options:
A)1 year
B)1 year 2 months
C)4 years 8 months
D)3 years
E)None
Rationale: Total decrease = 28 * 2 = 56 months
= 4 years 8 months
C
Answer: C
Question: A tap can fill a tank in 2 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)1 hr 40 min
B)4 hr
C)3 hr
D)1 hr 20 min
E)2 hr 50 min
Rationale: Explanation:
1 tap can fill the tank in 2 hours.
Therefore
1 tap can fill half tank in 1 hours.
3 taps can fill the tank in 2/3 hour.
Therefore
3 taps can fill half tank in 2/6 hour =20 minutes.
Total time taken=1 hour 20 minutes
Answer: Option D
Answer: D
Question: Given that E and F are events such that P(E) = 8, P(F) = 2 and P(E n F) = 8,
find P (E|F) and P(F|E)
Options:
A)5
B)4
C)12
D)36
E)98
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 8/8= 1
P(F|E) = P(EnF)/P(E) = 8/2 = 4.
B)
Answer: B
Question: Two good train each 900 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km / hr and 30 km /hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
Options:
A)12.2 sec
B)24.9 sec
C)86.4 sec
D)60.2 sec
E)None
Rationale: Sol.
Relative Speed = (45 + 30) km / hr
= (75 x 5 / 18) m/sec
= (125/6) m/sec.
Distance covered = (900 + 900) m = 1000 m.
Required time = (1800 x 6 / 125) sec = 86.4 sec.
Answer C
Answer: C
Question: A dice has one of the first 7 prime number on each its six sides ,with no two sides having the same number .the dice is rolled 12 times and the results added.the addition is most likely to be closet to
Options:
A)41
B)48
C)60
D)99
E)70
Rationale: if die is rolled then avg score = (2+3+5+7+11+13+17 )/7 = 58/7
so, most likely sum for 10 times = 58/7 * 12 = 99
ANSWER:D
Answer: D
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)99
C)88
D)66
E)21
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec.Answer: A
Answer: A
Question: A man has Rs. 416 in the denominations of one-rupee notes, five-rupee notes and ten rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
Options:
A)45
B)60
C)78
D)90
E)95
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 416
16x = 416
x = 26.
Hence, total number of notes = 3x = 78
Answer: Option C
Answer: C
Question: If 18 is 15 percent of 35 percent of a certain number, what is the number?
Options:
A)9
B)36
C)40
D)300
E)400
Rationale: Let the certain number be x.
=> (15/100)*(40/100)*x = 18;
=> x=300;
Ans is (D).
Answer: D
Question: The rupee/coin changing machine at a bank has a flaw. It gives 10 ten rupee notes if you put a 100 rupee note and 10 one rupee coins if you insert a 10 rupee note but gives 10 hundred rupee notes when you put a one rupee coin!Sivaji, after being ruined by his rivals in business is left with a one rupee coin and discovers the flaw in the machine by accident. By using the machine repeatedly, which of the following amounts is a valid amount that Sivaji can have when he gets tired and stops at some stage (assume that the machine has an infinite supply of notes and coins):
Options:
A)53947
B)53949
C)53946
D)53945
E)53944
Rationale: Explanation:
The process works like this:
Rs.1 Coin ⇒ 10 × 100 = Rs.1000
Rs.100 ⇒ 10 × 10
Rs.10 ⇒ 1 × 10
Sivaji gets more money when he inserts a rupee coin only. For each rupee coin he gets his money increased by 1000 times. Suppose he inserted 1 rupee coin and got 1000 rupees and again converted this into coins. So he ends up with 1000 coins. Now of this, he inserts one coin, he gets 1000. So he has 1999 with him. Now if he inserts another coin, he has 1998 + 1000 = 2998.
Now each of these numbers are in the form of 999n + 1. So option B can be written as 54 × 999 + 1.
Answer: B
Answer: B
Question: Pipe A can fill a tank in 3 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
Options:
A)4.5
B)17
C)18
D)19
E)12
Rationale: Let the leak can empty the full tank in x hours 1/3 - 1/x = 1/9
=> 1/x = 1/3 - 1/9 = (3 - 1)/9 = 2/9
=> x = 9/2 = 4.5.
Answer: A
Answer: A
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
Options:
A)Rs.3630
B)Rs.2840
C)Rs.3200
D)Rs.5600
E)Rs.3000
Rationale: Explanation:
6300:4200:10500
3:2:5
3/10 * 12100 = 3630
ANSWER IS A
Answer: A
Question: An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
Options:
A)90
B)80
C)40
D)50
E)89
Rationale: Total digits that can be formed = 10C1 * 10C1 = 100.
The digits that still remain digits when turned upside down are 0, 1, 6, 8 and 9.
So codes that can create confusion are:
01, 06, 08, 09
10, 16, 18, 19
60, 61, 66, 68 (69 would still be 69 when inverted)
80, 81, 86, 89
90, 91, 98, 99 (96 would still be 96 when inverted)
There are 20 such numbers.
Required numbers = 100 - 20 = 80
ANSWER:B
Answer: B
Question: If the product 4864 x 9 P 2 is divisible by 12, then the value of P is:
Options:
A)1
B)5
C)8
D)6
E)4
Rationale: Explanation:
Clearly, 4864 is divisible by 4.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
P = 1.
ANSWER A
Answer: A
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be
Options:
A)26
B)27
C)28
D)29
E)30
Rationale: Let number of hens = h and number of cows = c
number of heads = 48
=> h + c = 48 ---(Equation 1)
number of feet = 140
=> 2h + 4c = 140
=> h + 2c = 70 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 70 - 48
=> c = 22
Substituting the value of c in Equation 1, we get
h + 22 = 48
=> h = 48 - 22 = 26
i.e., number of hens = 26
Answer is A.
Answer: A
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 182, the sum due is:
Options:
A)s. 832
B)s. 968
C)s. 1960
D)s. 2400
E)s. 2800
Rationale: td=pw*r*t/100 so 182=pw*14*2/100 so pw=650
sum=pw+td..
sum=650+182=832
ANSWER:A
Answer: A
Question: Cuboid volume and Base area are 144 m^3 and 18m^3 respectively.Find the height of a cuboid?
Options:
A)5m
B)12m
C)6m
D)8m
E)10m
Rationale: Height of the cuboid=Volume* Base area
=144/18
=8 metre
Answer is option D
Answer: D
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)288
B)277
C)120
D)285
E)121
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Answer: C
Question: The average mark of 20 students in a class is 70 years. The average age of 10 students is 65. What is the total mark of remaining 10 students?
Options:
A)850
B)800
C)750
D)700
E)680
Rationale: Sum of the ages of 10 students
= (20 * 70) - (10 * 65) = 1400 - 650 = 750
Required Total marks = 750
Answer: C
Answer: C
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 6?
Options:
A)3/8
B)1/16
C)1/8
D)1/2
E)0
Rationale: One approach to solve the problem is to list the different possibilities for a toss of coin three times. Because there are two outcomes and the coin is tossed three times, the table will have 2*2*2 or 8 rows.
Next add the resulting rows together to find the sum (the fourth column in the table below).
Toss 1 | Toss 2 | Toss 3 | Sum
1 ---------- 1 -------- 1 ------ 3
1 ---------- 1 -------- 2 ------ 4
1 ---------- 2 -------- 1 ------ 4
1 ---------- 2 -------- 2 ------ 5
2 ---------- 1 -------- 1 ------ 4
2 ---------- 1 -------- 2 ------ 5
2 ---------- 2 -------- 1 ------ 5
2 ---------- 2 -------- 2 ------ 6
From the table we see that there are 0 situations where the sum of the tosses will be greater than 6. And there are 8 possible combinations resulting in a probability of
0/8 or a probability of 0.
SO the correct answer is E.
Answer: E
Question: Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 480. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
Options:
A)2:1
B)5:6
C)5:2
D)5:8
E)5:2
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 480 => x = 5000
Amount lent at 10% = 2000
Required ratio = 2000 : 1000 = 2:1
Answer:A
Answer: A
Question: If 4 and 8 are factors of 60n, what is the minimum value of n?
Options:
A) 2
B) 3
C) 8
D) 14
E) 56
Rationale: 60n/4*8 should be integer => 2*2*3*5*n/2*2*2*2*2 = 3*5*n/8must be an integer
for this to be true n must multiple of 8, thus min of n = 8
hence C
Answer: C
Question: In how many ways can be 3 boys and 3 girls sit around circular table so that no two boys sit next to each other?
Options:
A)(5!)^2
B)(6!)^2
C)3!2!
D)11!
E)(5!)^2*6!
Rationale: first fix one boy and place other 2 in alt seats so total ways is 3!
now place each girl between a pair of boys... total ways of seating arrangement of girls 3!
total is 2!*3!
ANS C
Answer: C
Question: A driving school claims an average test pass rate of 76.8 percent. What is the least number of pupils required to achieve this result?
Options:
A)125
B)113
C)189
D)153
E)142
Rationale: A
125
96 passes out of 125 give an average of 76.8% .
Answer: A
Question: If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)?
Options:
A)120
B)130
C)150
D)170
E)200
Rationale: (x + yi) / i = ( 7 + 9i )
(x + yi) = i(7 + 9i) = -9 + 7i
(x + yi)(x - yi) = (-9 + 7i)(-9 - 7i) = 81 + 49 = 130
CORRECT ANSWER IS B) 130
Answer: B
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)4 min
B)6 min
C)8 min
D)2 min
E)9 min
Rationale: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
Answer: A
Answer: A
Question: The difference of the cubes of two consecutive even integers is divisible by which of the following integers?
Options:
A)3
B)6
C)4
D)5
E)2
Rationale: Solution: let take 2 consecutive even numbers 2 and 4.
=> (4*4*4)-(2*2*2)=64-8=56 which is divisible by 4.
Answer C
Answer: C
Question: From a total of 5 boys and 5 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
Options:
A)16
B)24
C)60
D)100
E)240
Rationale: Answer=D=100
No of 4 person committees that can be formed=5C2*5C2=100
Answer D
Answer: D
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?
Options:
A) 3
B) 4
C) 5
D) 6
E) 7
Rationale: Given that (10a + b) - (10b + a) = 54 --> 9a - 9b =54 --> a - b = 6.
Answer: D.
Answer: D
Question: If x+y=280, x-y=200, for integers of x and y, y=?
Options:
A)200
B)240
C)50
D)115
E)150
Rationale: x+y = 280
x-y = 200
2x = 80
x = 40
y = 240
Answer is B
Answer: B
Question: How many multiples of 7 are there between 14 and 343, exclusive ?
Options:
A)48
B)47
C)46
D)45
E)44
Rationale: 7 * 2 = 14
7 * 49 = 343
Total multiples = (49-2) + 1 = 48
Exclude 7 343 = 48-2 = 46
Answer is (C)
Answer: C
Question: The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.7. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
Options:
A)0.8321
B)0.7
C)0.8108
D)0.7531
E)0.8213
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.75*80 = 60.
Out of 20 matches Matt does not play in, team wins 0.7*20 = 14.
So, out of 100 matches 60 + 14 = 74 are won.
It is known that the team has won the last match. Out of 74 matches won, Matt is in 60: 60/74 = 0.8108...
Answer: C.
Answer: C
Question: A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and captain) to a nearby port. Altogether, these passengers have 15 heads and 42 legs. How many cats does the ship host?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: sa's +co +ca +cats = 15. sa's + 1 +1 +cats =15 or sa's +cats =13.
sa's(2) +2 +2 +cats*4 =42 sa's*2 +cats*4 = 38 or sa's +cats*2 =19 or 13-cats +cat*2 =19
then cats =6
B
Answer: B
Question: What will come in place of the x in the following Number series? 6, 12, 21, x , 48
Options:
A)33
B)35
C)39
D)41
E)42
Rationale: (A)
The pattern is + 6, + 9, + 12, +15 ………..
So the missing term is = 21 + 12 = 33
Answer: A
Question: Sunil invested $ 1800 fir 2 years and $ 1400 for 3 years at the same rate of Simple Interest. If the total interest from these investments is $ 810, what is the rate of interest?
Options:
A)12 3/4%
B)25 1/3%
C)10 1/4%
D)8%
E)13 2/4%
Rationale: (1800x2xR)/100+(1400x3xR)/100=810
78R=810
R= 10 1/4%
Answer is C
Answer: C
Question: A shepherd has 1million sheep at the beginning of Year 2010. The no's grow by xx during the yr. A famine hits his village in the next year & many of his sheep die. The sheep population decreases by yy during 2001 and at the beginning of 2011 the shepherd finds that he is left with 1million sheep. Which of the following is correct?
Options:
A)x<y
B)x>y
C)x=y
D)x<=y
E)x>=y
Rationale: Let us assume the value of xx to be 10%10%.
Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10%10% of 1 million = 1.1 million
In 2001, the numbers decrease by y%y% and at the end of the year the number sheep in the herd = 1 million.
i.e., 0.1 million sheep have died in 2001.
In terms of the percentage of the number of sheep alive at the beginning of 2001,
it will be (0.1/1.1)×100%=9.09%(0.1/1.1)×100%=9.09%.
From the above illustration it is clear that x>y
B
Answer: B
Question: To furnish a room in a model home an interior decorator is to select 2 chairs and 2 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?
Options:
A)6
B)8
C)10
D)15
E)30
Rationale: Total number of ways to choose 2 chairs from 5= 5C2=10
Total number of combination=150
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C2=15..... 15*10=150
Answer is 6... A
Answer: A
Question: Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 10% and 10% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
Options:
A)10%
B)20%
C)21%
D)23%
E)Cannot be determined
Rationale: Answer: A.
Answer: A
Question: Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $3500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
Options:
A)$3,750
B)$5,600
C)$8,100
D)$15,000
E)$31,500
Rationale: x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $3500 triples to $10500, in 28 years, it will again triple to $10500*3=$31,500
Answer E
Answer: E
Question: If a man lost 5% by selling apples at the rate of 15 a rupee at how many a rupee must he sell them to gain 25%?
Options:
A)9.4
B)10.4
C)11.4
D)12.4
E)13.4
Rationale: 95% ---- 15
125% ---- ?
95/125 * 15 = 11.4
Answer: C
Answer: C
Question: A cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. Once the cistern is emptied, how much time will they take to fill it together completely?
Options:
A)12 minutes
B)12.5 min
C)14.4 min
D)10.2 min
E)14.66 min
Rationale: As pipe A takes 12min. to fill remaining one-third it takes 36min. to fill completely. similarly pipe B takes 24min. to fill completely
so, total time taken by both together is reciprocal of:
(1/36)+(1/24)=5/72
ans:14.4 min.
ANSWER:C
Answer: C
Question: An investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: 1 year: 100/3 = 33.33 approx $34: Total: 134
2nd year: 134/3 = 45: Total: 134+45 = 179
3rd year: 179/3 = 60: Total: 179+60 = 239
4th year: 239/3 = 80: Total: 239+80 = 319 > 3(100)
;4 years;
ANSWER:A
Answer: A
Question: In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?
Options:
A)2/3
B)5/8
C)3/5
D)4/7
E)4/9
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: B
Question: The function f is defined by subtracting 25 from the square of a number and the function a is defined as the square root of one-half of a number. If a(f(x))=10, then which of the following is a possible value of x?
Options:
A)-15
B)-5
C)0
D)5
E)25
Rationale: f(x) = x^2-25
a(x) = sqrt(x/2) not sqrt(x)/2, because the question clearly says its square root of (half of the number).
a(f(x)) = 10
a(x^2-25) =10
sqrt((x^2-25)/2) = 10
=> (x^2-25)/2 = 100
=>x^2 = 225
=> x = 15 or -15
Answer is A.
Answer: A
Question: The triplicate ratio of 1:2 is?
Options:
A)1:64
B)1:8
C)1:10
D)3:8
E)5:64
Rationale: 1^3: 2^3 = 1:8
ANSWER:B
Answer: B
Question: John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 170% of John's weight. Which of these 5 people weighs the least?
Options:
A)John
B)Susan
C)Sam
D)Mark
E)Lynn
Rationale: John weighs twice as much as Susan --> J=2S --> John cannot weigh the least;
Susan's weight is 60% of Sam's weight --> S=0.6*Sam --> Sam cannot weigh the least;
Mark weighs 50% of Lynn's weight --> M=0.5*L --> Lynn cannot weigh the least;
Lynn weighs 170% of John's weight --> L=1.9*J --> John cannot weigh the least (we already know that);
As you can see the answer is either Susan (S) or Mark (M). To compare their weights we should express their weights in regards of the same person: M=0.5*L=0.5*(1.7*J)=0.85*J and from J=2S, S=0.5*J --> Susan weights the least: Susan's weight is 50% of that of John and Mark's weight ismore than 50%of that of John.
Answer: B.
Answer: B
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options:
A)210
B)7200
C)1890
D)31970
E)10984
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= (7C3 x 4C2)
= 210.
ANSWER A 210
Answer: A
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
Options:
A)8
B)9
C)7
D)6
E)5
Rationale: Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer:A
Answer: A