mathewhe/aqua_rat huggingface dataset:
Question: A circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the earth dug out.
(A) 40m3
(B) 42m3
(C) 44m3
(D) 46m3
(E) 48m3
Rationale: Explanation:
Volume=πr2h
Volume=((22/7)∗1∗1∗14)m3
=44m3
ANSWER IS C
Answer: (C) 44m3
Question: A walks at 10 kmph and 6 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
(A) 100km
(B) 150km
(C) 50km
(D) 120km
(E) 200km
Rationale: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 6 hours.
x/10 - x/20 = 6
x = 120 km
Answer is D
Answer: (D) 120km
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
(A) 35.4 cm
(B) 32.4 cm
(C) 32 cm
(D) 30 cm
(E) 35 cm
Rationale: Explanation:
36/7 r = 6.3 = 32.4
ANSWER IS B
Answer: (B) 32.4 cm
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 16 seconds
(B) 76 seconds
(C) 26 seconds
(D) 12 seconds
(E) 18 seconds
Rationale: Speed of the boat downstream = 15 + 3
= 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m
= 60/5
= 12 seconds.
Answer: D
Answer: (D) 12 seconds
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 8 sec. What is the length of the fast train?
(A) 44 7/6 m
(B) 44 4/9 m
(C) 44 7/2 m
(D) 44 7/9 m
(E) 44 7/7 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 8 = 400/9 = 44 4/9 m.Answer:B
Answer: (B) 44 4/9 m
Question: (4.5 x 3.7 + 4.5 x 6.3)/(1.5 x 8.4 - 1.5 x 7.4) = ?
(A) 30
(B) 30.05
(C) 32
(D) 34
(E) 36
Rationale: Explanation:
(4.5 x 3.7 + 4.5 x 6.3)/(1.5 x 8.4 - 1.5 x 7.4)
= 4.5 x (3.7 + 6.3)/1.5 x (8.4 - 7.4)
= 4.5 x 10/1.5 x 1 = 30
Answer: Option A
Answer: (A) 30
Question: In a 4 person race, medals are awarded to the fastest 3 runners. The first-place runner receives a gold medal, the second-place runner receives a silver medal, and the third-place runner receives a bronze medal. In the event of a tie, the tied runners receive the same color medal. (For example, if there is a two-way tie for first-place, the top two runners receive gold medals, the next-fastest runner receives a silver medal, and no bronze medal is awarded). Assuming that exactly three medals are awarded, and that the three medal winners stand together with their medals to form a victory circle, how many C different victory circles are possible?
(A) 24
(B) 52
(C) 96
(D) 144
(E) 648
Rationale: Possible scenarios are:
1. Gold/Silver/Bronze/No medal (no ties) - 4!=24;
2. Gold/Gold/Silver/No medal - 4!/2!=12;
3. Gold/Silver/Silver/No medal - 4!/2!=12;
4. Gold/Gold/Gold/No medal - 4!/3!=4.
Total: 24+12+12+4=52
Answer: B.
Answer: (B) 52
Question: A train crosses a platform of 130 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) A)150m
(B) B)170m
(C) C)230m
(D) D)158m
(E) E)350m
Rationale: Length of the train be ‘X’
X + 130/15 = X + 250/20
4X + 520 = 3X + 750
X = 230m
Answer: C
Answer: (C) C)230m
Question: Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Tharak's age. After further 6 years, how many times would he be of Tharak's age?
(A) 1.52 times
(B) 1.83 times
(C) 2.83 times
(D) 0.83 times
(E) 6.2 times
Rationale: Assume that Tharak's present age =x.
Then, father's present age =3x+x=4x
After 8 years, father's age=2 1/2 times of Tharak' age
⇒(4x+8)=2 1/2(x+8)
⇒4x+8=5/2(x+8)
⇒8x+16=5x+40
⇒3x=40−16=24
⇒x=24/3=8
After further 6 years,
Sunil's age =x+6+6=8+6+6=20
Father's age =4x+6+6=4×8+6+6=44
Father's age/Sunil's age
=44/24
=1.83
ANSWER:B
Answer: (B) 1.83 times
Question: If a * b * c =(√(a + 2)(b + 3)) / (c + 1), find the value of 6 * 15 * 11.
(A) 8
(B) 5
(C) 1
(D) 3
(E) 4
Rationale: 6 * 15 * 11 = (√(6 + 2)(15 + 3) )/ (11 + 1)
= (√8 * 18) / 12
= (√144) / 12
= 12 / 124 = 1.
Answer is C
Answer: (C) 1
Question: For dinner at a restaurant, there are x+ 1 choices of appetizers, y main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
(A) x + y + z + 1
(B) xyz + xz
(C) xy + z + 1
(D) xyz + 1
(E) xyz + yz
Rationale: x + 1 appetizers,
y main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = yC1*(x+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = y(x+1)z = xyz + yz
Correct Option: E
Answer: (E) xyz + yz
Question: A number when divided by a certain divisor left remainder 255, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?
(A) 370
(B) 365
(C) 398
(D) 456
(E) 460
Rationale: Easy solution:
N= Dq1+255
2N = 2Dq1 + 51 0- (1)
2N = Dq2 + 112 - (2)
As (1) = (2) = 2N
D*(q2-2q1) = 398
D * Some integer = 398
Checking all options only (C) syncs with it.
Answer C
Answer: (C) 398
Question: In covering a distance of 24 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
(A) 4 kmph
(B) 6 kmph
(C) 6.25 kmph
(D) 7.5 kmph
(E) 7.8 kmph
Rationale: Let Abhay's speed be x km/hr.
Then,	24/X	-	24/2X	= 3
6x = 24
x = 4 km/hr. Answer: Option A
Answer: (A) 4 kmph
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
(A) 39
(B) 12
(C) 11
(D) 37
(E) 89
Rationale: Explanation:
16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: Option D
Answer: (D) 37
Question: What is the unit’s digit of 7^5
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: 7^1=7
7^2=49
7^3=343
7^4=1(last digit)
7^5=7(last digit) and the cycle repeats after every 4 powers
Therefore, last digit of 7^5=7
Answer D
Answer: (D) 7
Question: 20 people attend a party. 7 men are single and the rest are there with their wives. There are no children in the party. In all 10 women are present. Then the number of married men at the party is ?
(A) 5
(B) 3
(C) 7
(D) 8
(E) 9
Rationale: Total people = number of men + number of women
20 = 7 + number of married men + 10
number of married men = 20-10-7 = 3 men
ANSWER:B
Answer: (B) 3
Question: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 300 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
(A) 1.5%
(B) 1.9%
(C) 10%
(D) 15%
(E) 19%
Rationale: I think there is a typo in question.
It should have been "By weight Liquid 'X ' makes up..... "
Weight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B
When 300gms of A and 700gms of B is mixed :
Weight of Liquid X = (0.8 * 300)/100 + (1.8* 700)/100 = 15gms
% of Liquid X in resultant mixture = (15/1000) *100 = 1.5%
Answer : 1.5% ANSWER:A
Answer: (A) 1.5%
Question: Simplify: (10-5)-(-3+14-2)+(7-5)
(A) -1
(B) –2
(C) 1
(D) 2
(E) 0
Rationale: Solution:
(10-5)-(-3+14-2)+(7-5)
=5-(9)+2
=5-9+2
=-4+2
-2
Answer: (B)
Answer: (B) –2
Question: In an election, candidate A got 75% 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?
(A) 355600
(B) 355800
(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 = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
E)
Answer: (E) 357000
Question: Tom is chasing Jerry. In the same interval of time Tom jumps 8 times while Jerry jumps 6 times. But the distance covered by Tom in 7 Jumps is equal to the distance covered by Jerry in 5 Jumps. The ratio of speed of Tom and Jerry is:
(A) 48 :35
(B) 28 :15
(C) 24 :20
(D) 20 :21
(E) None
Rationale: Solution:
Given;
7 jumps of Tom = 5 jumps of Jerry.
Or, Tom / Jerry = 5/7;
Let Jerry's 1 leap = 7 meter and Tom's 1 leap = 5 meter.
Then, ratio of speed of Tom and Jerry = 8*5/6*7 = 40/42 = 20 :21.
Answer: Option D
Answer: (D) 20 :21
Question: A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years?
(A) 662.07
(B) 662.0
(C) 662.02
(D) 362.02
(E) 662.05
Rationale: Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]
= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02
Answer:C
Answer: (C) 662.02
Question: A large box contains 19 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
(A) 475
(B) 350
(C) 450
(D) 550
(E) 650
Rationale: The number of chocolate bars is equal to
19 * 25 = 475
correct answer A
Answer: (A) 475
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/9
(B) 5/4
(C) 5/1
(D) 5/6
(E) 5/2
Rationale: P(at least one graduate) = 1 - P(no graduates)
(6 * 5 * 4)/(10 * 9 * 8) = 5/6
Answer: D
Answer: (D) 5/6
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 50 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 2.4
(B) 3.2
(C) 4.0
(D) 4.8
(E) 5.6
Rationale: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 4.8 hours to travel 240 km, so C leaves 3.2 hours after A.
The answer is B.
Answer: (B) 3.2
Question: Mr.Govind invested an amount of Rs.13900 divided in two different schemes S1 and S2 at the simple interst rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in two years was Rs.3508, what was the amount invested in Scheme S2?
(A) Rs.6400
(B) Rs.6500
(C) Rs.7200
(D) Rs.7500
(E) Rs.7800
Rationale: Let the sum invested in Scheme S1 be Rs.x and that in Scheme S2 be Rs.(13900-x).
Then, (x*14*2)/100 + ((13900-x)*11*2)/100 = 3508;
28x-22x= 3350800-(13900*22);
6x = 45000; x= 7500
So sum invested in Scheme S2 = Rs. (13900-7500) = Rs.6400
ANSWER:A
Answer: (A) Rs.6400
Question: If x + (1/x) = 5, what is the value of E=x^2 + (1/x)^2?
(A) E=21
(B) E=22
(C) E=23
(D) 24
(E) 27
Rationale: Squaring on both sides,
x^2 + (1/x)^2 + 2(x)(1/x) = 5^2
x^2 + (1/x)^2 = 23
Answer: C
Answer: (C) E=23
Question: Let S be the set of permutations of the sequence 2, 3, 4, 5, 6 for which the first term is not 2. A permutation is chosen randomly from S. The probability that the second term is 5 is given by a/b (in lowest terms). What is a+b?
(A) 5
(B) 6
(C) 11
(D) 16
(E) 19
Rationale: The number of possible permutation without 2 in the first digit is
4X4X3X2X1=96 ways.
The number of possible permutations with 5 in the second term is= 3X3X2X1=18 ways.
18c1/96c1 = 18/96= 3/16= > a+b=19.
ANSWER:E
Answer: (E) 19
Question: The sum of three from the four numbers A, B , C , D are 3957 , 4012 , 4370 and 4374 What is the largest of the numbers A , B , C and D?
(A) 1614
(B) 1200
(C) 1560
(D) 1198
(E) 1298
Rationale: 3*(A+B+C+D)=3957+4012+4370+4374
A+B+C+D=5571
5571-(Least sum of 3 numbers)=Largest number
5571-3957=1614
so Largest number is 1614
ANSWER:A
Answer: (A) 1614
Question: John has to secure 60% marks to clear his exam of class 5th.
He got 10 marks and failed by 50 marks.
What is the maximum marks ?
(A) 110
(B) 105
(C) 100
(D) 95
(E) 90
Rationale: C
100
To pass the exam ravish needs 10 + 50 = 60 marks.
=> (60/60) *100 = 100
Answer: (C) 100
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 48 kmph, find the speed of the stream?
(A) 77
(B) 88
(C) 14
(D) 16
(E) 17
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 48/3 = 16 kmph.
Answer:D
Answer: (D) 16
Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
(A) 1101
(B) 1141
(C) 1120
(D) 1130
(E) None
Rationale: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
Answer B
Answer: (B) 1141
Question: Find the odd man out
36, 315, 612, 810, 966, 1362
(A) 966
(B) 612
(C) 315
(D) 36
(E) 1362
Rationale: 315is divisible by 3 which is odd number where as all others are even numbers divisible by 3.
ANSWER:C
Answer: (C) 315
Question: The price of raw materials has gone up by 15%, labour cost has also increased from 25% of the cost of raw material to 30% of the cost of raw material. By how much percentage should there be reduction in the usage of raw materials so as to keep the cost same?
(A) 28%
(B) 17%
(C) 27%
(D) 24%
(E) Cannot determined
Rationale: Solution: Let the initial cost of raw material be 100. So, initial labour cost was 25 and net cost was 125.
Now,
15% increment in raw materials cost and labour cost has gone up to 30% from 25 %.
Raw material cost = 115. And
Labour cost = (115 *30) = 34.5
So, New net cost,
= 115 + 34.5 = 149.5
%reduction = 24.5/149.5 = 17%(approx.)
Answer: Option B
Answer: (B) 17%
Question: If 40% of 3/5 of a number is 36, then the number is?
(A) 80
(B) 150
(C) 75
(D) 90
(E) None of these
Rationale: Let the number be x. Then 40% of 3/5 of x=36
40/100*3/5*x=36
x=(36*50/12)=150
Required number=150.
Correct Option: B
Answer: (B) 150
Question: A train 90 m long running at 56 kmph crosses a platform in 18 sec. What is the length of the platform?
(A) 190
(B) 200
(C) 180
(D) 881
(E) 271
Rationale: D = 56 * 5/18 = 25 = 280 – 90 = 190
Answer: A
Answer: (A) 190
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 52%
(B) 58%
(C) 82%
(D) 32%
(E) 12%
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
Answer: A
Answer: (A) 52%
Question: The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 5:4. If the oil bill for February had been $30 more, the corresponding ratio would have been 3:2. How much was the oil bill for January?
(A) $60
(B) $80
(C) $100
(D) $120
(E) $140
Rationale: 5:4 = 15:12 and 3:2 = 18:12.
An increase in $30 increases the ratio by 3:12.
Therefore an increase in $10 increases the ratio by 1:12.
Therefore, January's bill was 12($10) = $120.
The answer is D.
Answer: (D) $120
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.3200, what will be the difference between Q and R's share?
(A) 2788
(B) 4000
(C) 7282
(D) 2782
(E) 2729
Rationale: 4 --- 3200
5 --- ? => 4000
Answer:B
Answer: (B) 4000
Question: Data sufficiency question.
(A) 37
(B) 277
(C) 299
(D) 26
(E) 192
Rationale: Statement 1 has three solutions,(8, 0), (5, 1), (2, 2) but we cannot say precisely about the relationship
Statement 2 has three solutions, (8, 0), (5, 1), (2, 2) but we cannot say about the relationship.
So data insufficient.
Answer:B
Answer: (B) 277
Question: Today Joelle opened an interest-bearing savings account and deposited $5,000. If the annual interest rate is 4 percent compounded interest, and she neither deposits nor withdraws money for exactly 2 years, how much money will she have in the account?
(A) $5200
(B) $5408
(C) $5208
(D) $5608
(E) $5808
Rationale: Interest for 1st year = 5000*4/100 = 200
Interest for 2nd year = 5200 *4/100 = 208
Total =5000+200+208 = 5408
Answer : B
Answer: (B) $5408
Question: A boat can row 18 kmph in still water.It takes twice as long to row up as to row down the river.Find the rate of stream.
(A) 6 km/hr
(B) 7 km/hr
(C) 8km/hr
(D) 5 km/hr
(E) 9 km/hr
Rationale: still water-18kmph
It takes twice as long to row up as to row down the river.
then let upstream=2x and downstream=x
now buy the formulae
18=0.5(x+2X)----->x=12
so stream=0.5*(24-12)=6kmph
ANSWER:A
Answer: (A) 6 km/hr
Question: If e is an integer, what is the greatest possible value for e that would still make the following statement true: 11*10^e < 1/10 ?
(A)  –4
(B)  –3
(C)  –2
(D)  –1
(E)  0
Rationale: Just putting values, the LHS becomes
e=0 --> 11
e=-1 --> 11/10
e=-2 --> 11/100
e=-3 --> 11/1000
Anything lower will be smaller than 11/1000. e=-2, equality does not hold but it does for e=-3.
Answer is B.
Answer: (B)  –3
Question: Evaluate 50% of 450 + 45% of 500
(A) 232
(B) 450
(C) 252
(D) 262
(E) 272
Rationale: Explanation:
= (50/100) * 450 + (45/100) * 500
= 450
Option B
Answer: (B) 450
Question: Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 94% water by weight. What is the new weight of the cucumbers, in pounds?
(A) 2
(B) 16
(C) 92
(D) 96
(E) 98
Rationale: Out of 100 pounds 99% or 99 pounds is water and 1 pound is non-water. After somewaterevaporates the cucumbers become 94% water and 6% of non-water, so now 1 pound of non-water composes 6% of cucucmbers, which means that the new weight of cucumbers is 1/0.06=16 pounds.
Answer: B.
Answer: (B) 16
Question: If the radius of a circle is increased by 50% then the area is increased by:
(A) 44%
(B) 125%
(C) 144%
(D) 40%
(E) None of the above
Rationale: initially A=pi*r2
now R2=150/100r
then area=Pi*(150R/100)2
area=225R/100
that is area increases from 100 to 225=increase in area=125%
ANSWER:B
Answer: (B) 125%
Question: The market value of a certain machine decreased by 30 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
(A) $8,000
(B) $5,600
(C) $3,200
(D) $2,400
(E) $800
Rationale: Market value in 1982= $ 8000
Market value in 1983 = $ 8000- ($ 8000 x 30/100) = 8000-2400= $ 5600
Market value in 1984 = Market value in 1983 - (30 % of $8000)= 5600-2400 = $3200
ANSWER:C
Answer: (C) $3,200
Question: If an integer n is to be selected at random from 1 to 100, inclusive, what is probability n(n+1) will be divisible by 32?
(A) 2/7
(B) 3/7
(C) 1/16
(D) 1/14
(E) 1/12
Rationale: because n(n+1) is always an even product of even*odd or odd*even factors,
there is a probability of 1 that that it will be divisible by 2,
and, thus, a probability of 1/2 that it will be divisible by 4
and, thus, a probability of 1/4 that it will be divisible by 8
and, thus, a probability of 1/8 that it will be divisible by 16
and, thus, a probability of 1/16 that it will be divisible by 32
1*1/16=1/16
Answer : C
Answer: (C) 1/16
Question: Find the value of 72517 x 9999 = m?
(A) 345434667
(B) 246465757
(C) 465767867
(D) 725097483
(E) 645354643
Rationale: 72518 x 9999 = 72517 x (10000 - 1)
= 72517 x 10000 - 72517 x 1
= 725170000 - 72517
= 725097483
D
Answer: (D) 725097483
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
(A) 11
(B) 87
(C) 66
(D) 88
(E) 62
Rationale: (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
Answer: (D) 88
Question: A number n is chosen from {2, 4, 6 … 48}. The probability that ‘n’ satisfies the equation (2x – 6) (3x + 12) (x – 6) (x – 10) = 0 is
(A) 1/24
(B) 1/12
(C) 1/8
(D) 1/6
(E) 1/5
Rationale: Given, set is {2, 4, 6 … 48}
n(s) = 24
The roots of given equations are 3,4,4,10. The number of chosen from the set are 4, 10, which are the roots of given equation.
n(E) = 2
Therefore, required probability = 2/24 = 1/12.
ANSWER:B
Answer: (B) 1/12
Question: In a company, 56 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
(A) 45%
(B) 50%
(C) 55%
(D) 60%
(E) 65%
Rationale: The percent of employees who are unionized and men is 0.7*0.6 = 42%
The percent of employees who are unionized and women is 60 - 42 = 18%
44% of all employees are women, so non-union women are 44%-18% = 26%
40% of all employees are non-union.
The percent of non-union employees who are women is 26%/40% = 65%
The answer is E.
Answer: (E) 65%
Question: In Township K, 1/5 of the housing units are equipped with cable television . If 1/10 of the housing units , including 1/3 of those that are equipped with cable television , are equipped with videocassette recorders ,what fraction of the housing units have neither cable television nor videocassette recorders ?
(A) 23/30
(B) 11/15
(C) 7/10
(D) 1/6
(E) 2/15
Rationale: Let total Housing Units = 5x.
As per question, Equipped with Cable TV = x
Equipped with VCR = x/2, which includes x/3 CTV. So, only VCR = x/2 - x/3 = x/6.
So, Cable TV + VCR = x + x/6 = 7x/6
No Cable TV and VCR = 5x - 7x/6 = 23x/6.
Fraction = 23x/(6 * 5x) = 23/30. Hence, A
Answer: (A) 23/30
Question: Name the quadrant , if any , in which each point is locted.
(a) (1,6)
(b) (-4, -2)
(A) I, III
(B) I, IV
(C) III, IV
(D) V, III
(E) II, I
Rationale: (a) (1,6) ---I Quadrant
(b) (-4, -2) ---III Quadrant
Correct answer : (A)
Answer: (A) I, III
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is
(A) 16 years
(B) 88 years
(C) 39 years
(D) 66 years
(E) 77 years
Rationale: Let B's age = x years.
Then, As age = (x+ 9) years.
(x+9+10)=2(x—10)
hence x=39.
Present age of B = 39 years
Answer: C
Answer: (C) 39 years
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 1/2 of its present?
(A) 61.5
(B) 60.5
(C) 63.5
(D) 62.5
(E) 50
Rationale: Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 1x/2
Hence, number of buckets needed = 25x/(1x/2)=(25×2)/1=50
Answer is E.
Answer: (E) 50
Question: A fair silver coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
(A) A)37/256
(B) B)56/256
(C) C)65/256
(D) D)70/256
(E) E)81/256
Rationale: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.
8!/6!2! = 7*4 = 28
8!/7!1! = 8
8!/8! = 1
28 + 8 + 1 = 37/256
ans:A
Answer: (A) A)37/256
Question: Anand starts from a point P towards point Q, where PQ = 60 km. After 1 hour, Ram starts from P and catches up with Anand after 2 more hours. After meeting they continue to travel towards Q. On reaching Q, Ram reverses his direction and meets Anand 6 hours after the first meeting. Find Anand's speed.
(A) (45/7) kmph
(B) (60/7) kmph
(C) (40/7) kmph
(D) (30/7) kmph
(E) (65/7) kmph
Rationale: Let the first meeting point be at a distance of x km from P, the remaining distance until Q would be (60-x) km
Anand traveled this x kms in 3 hours, making his speed x/3 kmph
Ram traveled the same x kms in 2 hours, making his speed x/2 kmph
So, in 6 hours:
Anand will cover=6x/3=2x km
Ram will cover=6x/2=3x km
And between their first meeting point and second, they both together covered a distance of 2(90-x) km.
2x+3x=2(60-x)
5x=120-2x
7x=120
x=120/7 km
Anand's speed=x/3=120/(3*7)=40/7 kmph
Ans:C
Answer: (C) (40/7) kmph