divelab/Sys2Bench huggingface dataset:
Question: If the probability that the Cleveland Browns win the Super Bowl is 1/100 and the probability that the Cleveland Indians win the World Series is 1/10, what is the probability that either the Browns win the Super Bowl or the Indians win the World Series (but not both)?
Options:
A)9/50
B)17/100
C)27/250
D)53/500
E)101/1000
Rationale: 99/100*1/10 + 1/100*9/10 = 108/1000 = 27/250
The answer is C.
Answer: C
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the no. of heads. Find the total no.of buffaloes.
Options:
A)10
B)12
C)16
D)17
E)18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
B
Answer: B
Question: Calculate how much time could be saved if the train would run at its usual speed, given that it ran at 5/7 of its own speed and got to its destination in 15 hours?
Options:
A)1.29 hrs
B)2.29 hrs
C)4.29 hrs
D)5.29 hrs
E)3.29 hrs
Rationale: New speed = 5/7 of usual speed
New time = 5/7 of usual time
5/7 of usual time = 15 hrs
Usual time = 15*5/7 = 10.71 hrs
Time saved = 15-10.71 = 4.29 hrs
Answer is C
Answer: C
Question: Find the average of all the numbers between 6 and 34 which are divisible by 5
Options:
A)18
B)20
C)24
D)30
E)32
Rationale: Multiples of 5 between 6 and 34 are 10,15,20,25,30
Average = (10+15+20+25+30)/5
=5(10+30)/2*5
=40/2
=20
ANSWER:B
Answer: B
Question: What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
Options:
A)1000
B)2300
C)3000
D)4000
E)4500
Rationale: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
Answer: C
Question: A gardener increased the length of a rectangle-shaped garden by 25 percent and decreased its width by 10 percent. The area of the new garden
Options:
A)has increased by 15 percent
B)has increased by 12.5 percent
C)has increased by 7.5 percent
D)is exactly the same as the old area
E)cannot be expressed in percentage terms without actual numbers
Rationale: Let L be the original length and let W be the original width.
The original area was L*W.
The new area is 0.9W*1.25L = (0.9)(1.25)L*W = 1.125*L*W
The answer is B.
Answer: B
Question: An employer pays 3 workers P, Q and R a total of $610 a week. p is paid 125% of the amount Q is paid and 80% of the amount R is paid. How much does P earn in a week?
Options:
A)$150
B)$175
C)$180
D)$195
E)$200
Rationale: Soln:-
p+q+r = 610
given p=1.25q and p=.80r
putting these values in the above equation we get p=$200
ANSWER:E
Answer: E
Question: √289 - √625 ÷ √25 is equal to ?
Options:
A)17
B)15
C)12
D)-8/5
E)None
Rationale: Answer
√289 - √625 ÷ √25
= √17 x 17 - √25 x 25 ÷ √5 x 5
= 17 - 25 ÷ 5 = 17 - 5 = 12
Correct Option: C
Answer: C
Question: IF THE PROBABILITY is 0.6 that an “unfair” coin will turn up tails on any given toss. If the coin is tossed 3 times, what is the probability that at least one of the tosses will turn up tails?
Options:
A)0.064
B)0.36
C)0.64
D)0.784
E)0.936
Rationale: probability that at least one of the tosses will turn up tails = 1 - probability that all will be heads
= 1 - (0.4*0.4*0.4)
= 1 - 0.064
= 0.936 E
Answer: E
Question: A train covers a distance of 12 km in 10 minutes. If it takes 5 seconds to pass a telegraph post, then the length of the train is
Options:
A)110m
B)120m
C)140m
D)160m
E)100cm
Rationale: Explanation:
Speed =12/10x 60 km/hr = 72 x5/18m/sec = 20 m/sec.
Length of the train = (Speed x Time) = (20 x 5) m = 100 m
Answer: Option E
Answer: E
Question: If M:N = 3:5 and N:O = 5:8 then M:N:O is
Options:
A)6:7:8
B)2:7:8
C)3:7:9
D)4:7:8
E)3:7:8
Rationale: Solution:
M/N = 3/5;
N/O = 5/8;
M:N:O = 3*5:5*5:5*8 = 15:35:40 = 3:7:8
Answer: Option E
Answer: E
Question: Last year, the price of a vacation package was P. At the beginning of this year, the price went up 60%. Lucas used a travel voucher to purchase the vacation package at 25% off this year’s price. In terms of P, how much did Lucas pay?
Options:
A) P + 10
B) 1.1*P
C) 0.02*P
D) 0.20*P
E) 1.20*P
Rationale: Last year price = P;
This year price = 1.6P;
Lucas used a travel voucher to purchase the vacation package at30%offthis year’s price, thus he paid (1 - 0.25)*1.6P = 1.20P.
Answer: E.
Answer: E
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 8% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)64.54
B)62.6
C)62.1
D)62.7
E)62.2
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(92/100) = 59.375
MP = 64.54
Answer: A
Answer: A
Question: Ten boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
Options:
A)A)10^30
B)B)2^30
C)C)1^30
D)D)3^30
E)E)6^30
Rationale: Each Mango can be given to any one of the Ten people or in other words..1 mango can be divided into 10 ways...so all 30 can be divided in 10^30 ways
ANS:A
Answer: A
Question: Solve for x the equation log9(x3) = log2(8)
Options:
A)9
B)8
C)7
D)6
E)5
Rationale: log9(x3) = log2(8) : given
log2(23) = 3 : simplify right hand side of given equation.
log9(x3) = 3 : rewrite the above equation
log9(x3) = log9(93) : rewite 3 as a log base 9.
x3 = 93 : obtain algebraic equation from eqaution D.
x = 9 : solve above for x
correct answer A
Answer: A
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
Options:
A)4830
B)5120
C)6420
D)8960
E)None
Rationale: EXPLANATION
Clearly, l = (48 – 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
Answer B
Answer: B
Question: A sequence contains an alternation of positive and negative numbers. The sequence contains x numbers, and begins with a positive number. How many positive numbers are in it If x is an odd number?
Options:
A)(x+1)/2
B)x/3
C)x/(2-1)
D)x/(2+1)
E)(x-1)/2
Rationale: Lets put values for x, say x=7 since it's odd
and first number is neg so sequence will be {pos,neg,pos,neg,pos,neg,pos} we can see that it has 4 positive terms
so putting x=7 in the options,
option A = (x+1)/2 => (7+1)/2 = 4 , the number of positive integers
So, A is the answer
Answer: A
Question: The average length of 6 ropes is 80 cm. If the average length of one third of the ropes measure to 70 cm, what is the average of the other ropes?
Options:
A)75.
B)85.
C)90.
D)94.
E)100.
Rationale: Edit:
Given ( X1 + X2 ... + X6 ) / 6 = 80
( X1 + X2 ... + X6 ) = 480 --> Eq 1.
Now given avg length of one third ropes is 70. That means out 6 / 3 = 2 ropes.
let the avg length of two ropes be ( X1 + X2 ) / 2 = 70 .
( X1 + X2 ) = 140. --> eq 2.
Now we are asked to find the average of the remaining i.e. ( X3 + X4 + X5 + X6 )
Substitute eq 2 in eq 1 then we get
140 + X3 + X4 + X5 + X6 = 480
=> X3 + X4 + X5 + X6 = 340
Now divide 340 by 4 we get 85.
=> ( X3 + X4 + X5 + X6) / 4 = 85 = avg length of remaining ropes.
IMO correct option is B.
Answer: B
Question: If x and y are even integers, which of the following is an odd integer?
Options:
A)xy + 2
B)x(y − 1)
C)x(x + 5)
D)3x + 4y
E)(x + 3)(y − 1)
Rationale: If x and y are even integers, then:
A. xy + 2: even + even = even
B. x(y − 1): even(odd) = even
C. x(x + 5): even(odd) = even
D. 3x + 4y: even + even = even
E. (x + 3)(y − 1): (odd)(odd) = odd.
Answer is E.
Answer: E
Question: If the complement of a certain angle is five times the measure of that certain angle, then what is the measure of that certain angle?
Options:
A)45°
B)30°
C)22.5°
D)18°
E)15°
Rationale: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 5x, and together, these add up to 90 degrees.
x + 5x = 90
6x = 90
x = 15°
Answer = (E)
Answer: E
Question: Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 55, and the three numbers in order are?
Options:
A)116,58,36
B)90,45,30
C)126,63,36
D)108,54,36
E)None of these
Rationale: Explanation :
Solution: Let A =x,
B =x/2, C = x/3.
=x + x/2 + x/3 / 3 = 55
By solving we will get x = 90.
Hence A= 90
B= 90/2= 45
C= 90/3 = 30
Answer : B
Answer: B
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Options:
A)4
B)8
C)6
D)2
E)10
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
So Age of the youngest child = x = 4 years.
ANSWER A
Answer: A
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
Options:
A)76
B)42
C)78
D)26
E)92
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B
Answer: B
Question: A group of 8 employees book a full row at a movie theater. There are 2 best buddies and a couple and the 2 people in both those cases must always sit together. in how many arrangements can the students sit?
Options:
A)A.1296
B)B.2880
C)C.1850
D)D.3546
E)E.4200
Rationale: If we Glue the best buddy and couple together: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each couple within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: B.
Answer: B
Question: In seventeen given numbers, the average of first 9 numbers is 4 and that of the last 9 numbers is also 4. If the average of these 17 numbers is 3, the 9th number is
Options:
A)23
B)4
C)17
D)21
E)28
Rationale: Explanation :
9th number = (9*4 + 9*4 - 17*3)
= 21.
Answer : D
Answer: D
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Options:
A)2888
B)2778
C)2500
D)2818
E)2871
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500.AnswerC
Answer: C
Question: The average of 6 no.'s is 3.95. The average of 2of them is 4.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
Options:
A)4.2
B)4.4
C)3.6
D)5.6
E)5.7
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(4.4 * 2) + (3.85 * 2)]
= 7.20.
Required average = (7.2 / 2) = 3.6.
C
Answer: C
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.20,000 earned at the end of 2years from the startingof the business?
Options:
A)s. 5,000
B)s. 5,500
C)s. 5,700
D)s. 6,000
E)s. 7,500
Rationale: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 20000 x	3/10	= Rs. 6,000.
D
Answer: D
Question: Diesel costs Rs.4 per lit and petrol costs 7.23 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol.
Options:
A)9 months
B)5 months
C)7 months
D)3 months
E)2 months
Rationale: Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85
=>In the fifth Month the price of the diesel would be 5.85*110/100 = 6.44
=>In the sixth Month the price of the diesel would be 6.44*110/100 = 7.08
=>In the seventh Month the price of the diesel would be 7.08*110/100 = 7.79 which is higher than the price of petrol
Answer : C
Answer: C
Question: The ratio, by volume, of bleach to detergent to water in a certain solution is 2 : 25 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?
Options:
A)40
B)45
C)50
D)75/2
E)35
Rationale: B:D:W = 2:25:100
Bnew / Dnew = (1/3)*(2/25) = (2/75)
Dnew / Wnew = (1/2)*(25/100) = (1/8)
Wnew = 300
Dnew = Wnew/5 = 300/8 =75/2
So, answer will be D
Answer: D
Question: In digging a pond 20 m * 12 m * 5 m the volumes of the soil extracted will be?
Options:
A)3387
B)1000
C)1200
D)2787
E)1121
Rationale: 20 * 12 * 5 = 1200
Answer: C
Answer: C
Question: The average of 45 results is 10. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result?
Options:
A)600
B)480
C)750
D)650
E)560
Rationale: 23th result = sum of 45results - sum of 44 results
10*45-15*22+20*22 = 450-330+440 = 560
Answer is E
Answer: E
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)8 sec
B)12 sec
C)15 sec
D)10 sec
E)11 sec
Rationale: Speed of the first train = 120/10 m/sec = 12 m/sec.
Speed of the second train = 120/15 m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Required time = (120 + 120)/20 sec = 12 sec.
Answer : B.
Answer: B
Question: The average of a couple was 23Yrs when they were married 5Yrs ago.The avg age of
the couple and a child, who was born during the interval, is 20Yrs now. How old is the
child now ?
Options:
A)2 Yrs
B)4 Yrs
C)3 Yrs
D)1 Yrs
E)None of these
Rationale: (a+b-5-5)/2=23;
a+b=56;
a+b+c/3=20;
solving both c=4
ANSWER:B
Answer: B
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Options:
A)38020
B)38000
C)38028
D)38019
E)38192
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100)
=38000
Answer: B
Answer: B
Question: A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
Options:
A)7 days
B)9 days
C)4 days
D)6 days
E)2 days
Rationale: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3.
Total time required to complete the work = 2 * 3
= 6 days.
Answer: D
Answer: D
Question: What approximate value should come in place of the question mark (?) in the following equation?
95.245 + 25.912 × 7.2 + ? = 905.293
Options:
A)986.6
B)936.6
C)996.6
D)995.6
E)998.6
Rationale: 95.245 + 25.912 × 7.2 + ? = 905.293
or, ? = 905.293 – 95.245 + 25.912 × 7.2
? = 905.293 – 95.245 + 186.5664
≈ 996.6
Answer C
Answer: C
Question: If a number between 10 and 30 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
Options:
A)31/41
B)4/21
C)14/41
D)27/41
E)11/41
Rationale: If tens digi is 3 ---> ones digit : 0,
If tens digi is 2 ---> ones digit : 0, 1
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 30-10+1=21.
So the probability is 4/21.
The answer is (B).
Answer: B
Question: Find the ones digit of 73^351
Options:
A)3
B)5
C)6
D)7
E)9
Rationale: The units digit of 73^351 will be the same as the units digit of 3^351
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 351=348+3=(multiple of 4)+3, then the units digit of 3^351 will be the third number in the pattern thus 7.
Answer: D.
Answer: D
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
Options:
A)Rs.146
B)Rs.144
C)Rs.129
D)Rs.123
E)Rs.128
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100
= Rs.144
Answer:B
Answer: B
Question: A man took some money for borrowed, for 2 years the total will be Rs.9000/- and 5 years it will be13, Rs.500/-. Then how much amount he borrowed?
Options:
A)Rs.5000/-
B)Rs.5200/-
C)Rs.5500/-
D)Rs.5800/-
E)Rs.6000/-
Rationale: 2 years --------> Rs.9000/-
5 years --------> Rs.13500/-
~ ~
------------------------------
3 years ---------> Rs.4500/-
1 year ----------> Rs.1500/-
2years * Rs.1500/- = Rs.3300/-
P = Rs.9000/- - Rs.30000/- = Rs.6000/-
P = Rs.6000/-
E
Answer: E
Question: A car travels at a speed of 10 miles per hour. How far will it travel in 5 hours?
Options:
A)50 miles
B)62 miles
C)325 miles
D)70 miles
E)20 miles
Rationale: During each hour, the car travels 65 miles. For 5 hours it will travel
10 + 10 + 10 + 10 + 10 = 5 *10 = 50 miles correct answer A
Answer: A
Question: Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 90kmph. When will Raghu overtake Anup?
Options:
A)9:00am
B)9:40am
C)10:00am
D)12:00pm
E)11:10am
Rationale: Suppose bike is overtaken by car xhrs after 6am
Distance covered by the bike in x hrs = distance covered by the car in x-1 hr
60x = 90(x-1)
30x = 90
x = 3 hrs
Required time = 6+3 = 9:00am
Answer is A
Answer: A
Question: A shopkeeper buys mangoes at the rate of 7 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)33 4/3 %
B)33 1/7 %
C)400/7 %
D)32 1/3 %
E)33 2/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 21.
If he buys 7 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 7
Profit = SP - CP = 7 - 3 = 4
Profit Percent = 4/7 * 100 = 400/7 %
Answer:C
Answer: C
Question: An apple tree has 30 apples. 10 apples have fallen off of the tree. How many apples remain on the tree?
Options:
A)20
B)1
C)0
D)5
E)100
Rationale: A. 20
Answer: A
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
Options:
A)537
B)528
C)645
D)538
E)538
Rationale: Assume X soldiers join the fort. 1200 soldiers have provision for 1200(days for which provisions last them)(rate of consumption of each soldier)
= 1200(30)(3) kg
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) kg
As the same provisions are available
=> 1200(30)(3) = (1200 + x)(25)(2.5)
x = [1200(30)(3)]/[(25)(2.5)] - 1200
Answer:B
x = 528
Answer: B
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 67.12 = ?
Options:
A)230
B)231
C)235
D)220
E)240
Rationale: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 67.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 67.12
= 256.3 + 40.3 – 67.12 ≈ 231
Answer B
Answer: B
Question: Find the least number by which (59)(36)(17) has to be multiplied to obtain a perfect square?
Options:
A)5
B)17
C)85
D)221
E)223
Rationale: For any perfect square the index of the power of each of its prime factors is even. in the given number the power of 5 and 17 have odd indices, while 3 has an even index.
The least number = (5)(17) = 85.
ANSWER:C
Answer: C
Question: What is the least value of x. So that 43x87 is divisible by 3?
Options:
A)4
B)5
C)2
D)6
E)7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
4 + 3 + x + 8 + 7 = 22 + x
Least value of x may be 2
Therefore 22+ 2 = 24 is divisible by 3.
C
Answer: C
Question: The average salary per head of the entire staff of an office including the officers and clerks is Rs.90. The average salary of officers is Rs.600 and that of the clerks is Rs.84. If the number of officers is 2, find the number of officers in the office?
Options:
A)1
B)8
C)7
D)6
E)2
Rationale: 6 * 22 = 132
7 * 19 = 133
--------------
1.Answer: A
Answer: A
Question: (1+0.0001)/(0.00004+1)
The value of the expression above is closet to which of the following?
Options:
A)0.0001
B)0.001
C)0.1
D)1
E)10
Rationale: Notice that we need approximate value of the fraction.
Now, the nominator is very close to 1 and the denominator is very close to 1, hence the value of the fraction is very close to 1/1=1.
Answer: D.
Answer: D
Question: 49 * 49 * 49 * 49 = 7?
Options:
A)4
B)5
C)7
D)9
E)8
Rationale: Sol.
49 * 49 * 49 * 49 = (72 * 72 * 72 * 72) = 7(2+2+2+2) = 78.
So, the correct answer is 8.
Answer D
Answer: D
Question: One fourth of a solution that was 10% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
Options:
A)24%
B)34%
C)22%
D)18%
E)8.5%
Rationale: Say the second solution (which was 1/4 th of total) was x% salt , then 3/4*0.1+1/4*x=1*0.16 --> x=0.34. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.16 --> x=0.34.
Answer: B.
Answer: B
Question: If a, b, c are consecutive positive integers and b<a<c, which of the following must be true?
I. c-b=2
II. abc is an even integer
III. (a+b+c)/3 is an integer
Options:
A)I
B)II
C)I and II
D)II and III
E)I, II and III
Rationale: 1. c-b=2 --> b, a, c are consequitive positive integers and a<b<c then c=b+2 --> c-b=2. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/4 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. Or: (a+b+c)/4=fraction.
Answer: C.
Answer: C
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 7 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
Options:
A)9:30am
B)10:30am
C)11:30am
D)10:40am
E)10:50am
Rationale: In 7 hours the inlet pipe will pump in water equal to 7*1/5 = 7/5 of the pool. So, 2/5 more than necessary, which should be compensated by the outlet pipe. To pump out 2/5 of the water the outlet pipe needs 30/5 = 6 hours.
Therefore, the outlet pipe should be opened at 9:30am + 7 hours - 6 hours = 10:30am.
Answer: B
Answer: B
Question: The largest 4 digit number exactly divisible by 88 is?
Options:
A)9768
B)9750
C)9468
D)9568
E)9944
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
E)
Answer: E
Question: An entrance exam question paper consists of five problems, each problem having three choices. In how many ways can a student attempt one or more problems?
Options:
A)500
B)1023
C)1024
D)1035
E)1300
Rationale: paper 5 problems and each 3 choices so no of ways = 4^5 -1
= 2^10 - 1 = 1024 - 1 = 1023
ANSWER B
Answer: B
Question: A man can hit a target once in 5 shots. If he fires 4 shots in succession, how many ways that he will hit his target?
Options:
A)71/234
B)81/133
C)81/343
D)34/83
E)91/324
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 - 1/5 = 4/5
Therefore, the probability that he will not hit the target in any of the four shots = 4/5^4 = 34/83
D
Answer: D