divelab/Sys2Bench huggingface dataset:
Question: In 1982 and 1983, Company B’s operating expenses were $12.0 million and $15.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?
Options:
A)3%
B)5 5/9%
C)25%
D)33 1/3%
E)60%
Rationale: Profit in 1982 = 15.6 - 12 = 3.6 million $
Profit in 1983 = 18.8 - 15 = 3.8 million $
Percentage increase in profit = (3.8-3.6)/3.6 * 100 %
= 5 5/9 %
Answer B
Answer: B
Question: A start walking from a place at a uniform speed of 5 kmph in a particular direction. After half an hour, B starts from the same place and walks in the same direction as A at a uniform speed and overtakes A after 1 hour 48 minutes. Find the speed of B.
Options:
A)4.7 kmph
B)5.6 kmph
C)4 kmph
D)7 kmph
E)5.3 kmph
Rationale: Distance covered by A in 30 min = 1 Km
B covers extra 1km in 1 hour 48 minutes (9/5 hr)
i.e. Relative speed of B over A = 1/(9/5) = 5/9
So the speed of B = Speed of A + 5/9
= 5 + 5/9
= 5.55
Answer B
Answer: B
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is
Options:
A)87.5 km/h
B)66.5 km/h
C)42.5 km/h
D)32.5 km/h
E)61.5 km/h
Rationale: A
87.5 km/h
Answer: A
Question: what is the total number of factor of 16!
Options:
A)4376
B)5376
C)6376
D)7376
E)8376
Rationale: 16! = 2^15 * 3^6 * 5^3 * 7^2 * 11^1 * 13^1
total number of factors = (15+1)*(6+1)*(3+1)*(2+1)*(1+1)*(1+1) = 5376
ANSWER:B
Answer: B
Question: 123 typists typeed 984 papers in 1/15 hour. The number of papers typed for minute by a average typist is
Options:
A)7
B)2
C)4
D)5
E)9
Rationale: Explanation:
Use unitary method:
{1}{15} hours, 123 typists can type 984 paper
123 typists can type e \frac{984}{4} = 246 papers
1 typist can typefrac{246}{123} =2 papers [ Hint{1}{15} hours = 4 minutes]
Answer: B
Answer: B
Question: A project scheduled to be carried out over a single fiscal year has a budget of $12,600, divided into12 equal monthly allocations. At the end of the sixth month of that fiscal year, the total amount actually spent on the project was $6,580. By how much was the project over its budget?
Options:
A) $380
B) $540
C) $280
D) $1,380
E) $1,430
Rationale: Difficulty level: 600
Each month's budget = 12600/12 = 1050
Budget for 6 months = 6*1050 = 6300
Actual amount spent = 6580
Amount spent over the budget = 6580 - 6300 = 280
Answer (C),
Regards,
Answer: C
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $110, how much more remains to be paid?
Options:
A)$880
B)$990
C)$1,000
D)$1,100
E)$1,210
Rationale: 10/100P = 110 >> p= 110*100/10 = 1100
1100 - 110 = 990
ANSWER:B
Answer: B
Question: Mother,her daughter and her grand child weighs 160 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
Options:
A)46
B)47
C)48
D)49
E)40
Rationale: mother + daughter + child = 160kg
daughter + child = 60kg
mother = 160 - 60 = 100kg
child = 1/5th of mother = (1/5)*100 = 20kg
So now daughter = 120 -(mother + child) = 160 - (100+20) = 40kg
ANSWER:E
Answer: E
Question: An alloy weighing 18 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?
Options:
A)6
B)90
C)12
D)24
E)48
Rationale: In 24 ounces, gold is 18 * (70/100) = 12.6 ounces. Now we add x ounces of pure gold to make it 90% gold.
So 12.6 + x = (24 + x)* 90/100 => x =90.
Answer is B.
Answer: B
Question: A box contains six bulbs out of which 3 are defective. If three bulbs are chosen at random, find the probability that all the three bulbs are defective?
Options:
A)1/12
B)1/20
C)1/29
D)1/36
E)1/26
Rationale: Out of six, three are good and three are defective. Required probability
= 3C3/6C3
= 1/20
Answer:B
Answer: B
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 35 years. The ratio of their ages after 8 years will be
Options:
A)28 : 23
B)6 : 11
C)5 : 4
D)3 : 5
E)7 : 11
Rationale: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x= 35
x = 5
Mini’s age = 20 years
And Minakshi’s age = 15 years
Ratio of their ages after 8 years = (20 + 8) : (15 + 8) = 28 : 23
ANSWER:A
Answer: A
Question: Who is to the immediate right of E?
Options:
A)221
B)II only
C)I and II
D)I and III
E)II and III
Rationale: Answer:A
Answer: A
Question: A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 20% less than B, and C costs 25% less than A,and D costs 45% less than C what percent of B's cost is D?
Options:
A)40%
B)33%
C)44%
D)36%
E)42%
Rationale: Soln:-
B=100
A 20% less than B = 80
C 25% less than A = 60
D 45% less than C = 33
D is what percent of B = D/B * 100
= 33/100 * 100 = 33%
ANSWER:B
Answer: B
Question: Meg and Bob are among the 6 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
Options:
A)24
B)30
C)360
D)90
E)120
Rationale: Total # of ways the race can be finished is 6!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 6!/2=360.
Answer: C.
Answer: C
Question: A field of 40 meter long and 35 metre wide.The field is surronded by a path of uniform width of 2.5 metre runs round it on the outside.Find the Volume of the path?
Options:
A)Cannot be determine
B)400
C)500
D)100
E)250
Rationale: answer is option A.
we cannot determine the volume for the path.
Answer: A
Question: How many ways the three digits number (XYZ) can be formed in the form XZ?
Options:
A)540
B)550
C)554
D)566
E)576
Rationale: take value of X Y Z in 0 -9
here value of x cant be 0 as its in cent place.
take value of x - 1 to 9
y -- 0 -9
z -- 0 - 9
now put x =1 y = 0 then z = 0 to 9 here we cant use 1 for y and 1 and 0 for z.
1 0 2, 10 3, 10 4, 105, 106, 107, 108, 109
so for x = 9 value possible and for z = 8 ---so total value possible are 72 and in y we can put different 8 values so answer is 9 * 8 * 8 == 64*9= 576
ANSWER:E
Answer: E
Question: 54671 - 14456 - 33466 = ?
Options:
A)2449
B)5449
C)6749
D)6449
E)6468
Rationale: C
If we calculate we will get 6749
Answer: C
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.157 per kg, the price of the third variety per kg will be
Options:
A)Rs.179.50
B)Rs.1700
C)Rs. 175.50
D)Rs. 180
E)None
Rationale: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-157/22.50 = 1 =â€º x - 157 = 22.50 =â€º x=179.50.
Hence, price of the third variety = Rs.179.50 per kg.
Answer A
Answer: A
Question: Two positive integers differ by 4, and sum of their reciprocals is 1. Then one of the numbers is
Options:
A)2
B)b) 1
C)c) 5
D)d) 21
E)e) 28
Rationale: Algebraic approach:
Let n be the smaller integer => 1/n + 1/(n+4) = 1 or ((n+4)+n)/n(n+4) =1 or n^2+4n =2n+4 or n=2 as n cannot be -negative
Solve for n => n=2. Hence,
A
Answer: A
Question: 60 percent of movie theatres in Town X have 1 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 56 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
Options:
A)12
B)18
C)32
D)40
E)44
Rationale: Lets take numbers here.
Assume that the total number of movie theaters in the town = 100
Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12
Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44
Of these 44 theaters, 12 are those with 3 screens or less
Therefore 40 (44-12) must be those with four screens or more
D is the answer
Answer: D
Question: In how many different ways can be letters of the word SOFTWARE be arranged in such a way that the vowels always come together?
Options:
A)13440
B)1440
C)360
D)120
E)None of these
Rationale: When the vowels are always together, then treat all the vowels as a single letter and then all the letters can be arranged in 6! ways and also all three vowels can be arranged in 3! ways. Hence, required no. of arrangements = 6! × 3! = 4320.
Answer E
Answer: E
Question: How many integers from 1 to 100 (both inclusive) have odd number of factors?
Options:
A)7
B)8
C)9
D)10
E)Greater than 10
Rationale: All perfect squares have odd # of factors. Squaring integers 1-10 produces 1, 4, 9, 16, ... 100 which all have odd # of factors. Answer is D
Answer: D
Question: 10 men can complete a piece of work in 35 days. In how many days can 7 men complete that piece of work?
Options:
A)23 days
B)46 days
C)22 days
D)29 days
E)50 days
Rationale: E
50 days
10 * 35 = 7 * x => x = 50 days
Answer: E
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Options:
A)28%
B)40%
C)64.8%
D)70%
E)81%
Rationale: original price = 100
day 1 discount = 10%,price = 100-10 =90
day 2 discount = 10%,price = 90-9=81
day 3 discount = 10%,price = 81-8.1= 72.9
which is 72.9/90 *100 of the sale price on day 1= ~81%
Answer E
Answer: E
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
A)287 cm2
B)150 cm2
C)1678 cm2
D)776 cm2
E)678 cm2
Rationale: 1/2 * 20(9 + 6)
= 150 cm2
Answer: B
Answer: B
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of
the boat in still water is
Options:
A)12 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)None of these
Rationale: Explanation:
Rate upstream = (7/42)*60 kmh = 10 kmph.
Speed of stream = 3 kmph.
Let speed in still water is x km/hr
Then, speed upstream = (x �3) km/hr.
x-3 = 10 or x = 13 kmph
Answer: B
Answer: B
Question: One soap can be made out of the scraps obtained while preparing 11 soaps. How many soaps can be prepared out of the scrap obtained out of 251 soaps. (Take all possibilities)
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: From 242 soap scraps, we can make 242/11 = 22 soaps., which results in two more soaps. So, it now becomes 24 soaps and scraps of 2 soaps from 242 soaps. From the scrap of remaining 9 (=251-242) soaps, and together with the scraps of the two soaps already present, we can prepare one more soap. So total 25 soaps are possible.
ANSWER:B
Answer: B
Question: Which of the following is the sum of all the even numbers between 1 and 91, inclusive?
Options:
A)2550
B)2450
C)2600
D)2499
E)2446
Rationale: This question can be solved withbunching.
We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 2, 4, 6, 8.....98.
If you take the next smallest and next biggest numbers, you have...
10+90 = 100
This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs...
44+56 = 100
46+54 = 100
48+52 = 100
There IS a middle number: 50; this number does NOT get paired up.
Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50 -4= 2446
Final Answer:
E
Answer: E
Question: In a group of 8 engineers, 3 engineers have a PHD degree; the others have only an MS or BS degree. A team of 3 engineers is to be chosen which must have at least 1 engineer with a PHD, how many different teams can be chosen?
Options:
A)56
B)46
C)64
D)65
E)10
Rationale: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 8
r = 3
So, total teams is 8C3 = 8!/(3!(8 - 3)!) = 56, and
n = 8 - 3 = 5
r = 3
for teams without a PHD is 5C3 = 5!/(3!(5 - 3)!) = 10,
so, teams with at least 1 PHD = 56 - 10 = 46
Answer: B
Answer: B
Question: A toothpaste manufacturer has set an annual production target to gain more profits. This year the target reached is 1/10 of last year's target. If the target production this year is increased 5% of the last year's target, how much percentage of the last year's target does he still need to reach to get the profit?
Options:
A)4/5
B)3/6
C)20/20
D)10/5
E)4/3
Rationale: Given 1/10 and 5% that is 1/10
Let the last year's target be 20
This year's target is 5% more of last year=22
The target reached this year=1/10*20=2
Remaining target is 22-2=20
Required 20/20
Answer (C)
Answer: C
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.5 per sq m?
Options:
A)3350
B)3357
C)3328
D)3329
E)3375
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 5 = Rs.3375
Answer:E
Answer: E
Question: What is the units digit of 17^83 × 13^52 × 11^87?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: To find : the units digit of 17^83 × 13^82 × 11^87
Let's reduce the clutter and simplify the product
(7^83) (3^82) (1^87)
7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4th power
so 7^5 has the same last digit as 7^1, 7^9, 7^13
Thus , 7^83 has the same last digit as 7^3, 7^7, 7^11 i.e.3
3 has a cyclicity of 4 : exactly the same routine as above
Thus , 3^82 has the same last digit as 3^2, 3^6, 3^10 i.e.9
Any power of 1 will result in1as the last digit
So, product of our last digits = 3 x 9 x 1 = 27....last digit is 5
Correct Option : B
Answer: B
Question: The sum of two numbers is 50 and their difference is 10. Find their product.
Options:
A)600
B)114
C)315
D)325
E)335
Rationale: Let the numbers be x and y.
Then x + y = 50 and x - y = 10
x = 30; y = 20
xy = 30 * 20= 600
ANSWER:A
Answer: A
Question: Which of the following has most number of divisors?
Options:
A)99
B)101
C)176
D)182
E)None of these
Rationale: 99=1*3*3*11; 101=1*101
176=1*2*2*2*2*11; 182=1*2*7*13;
So, divisors of 99 are 1,3,9,11,33 and 99;
divisors of 101 are 1 and 101;
divisors of 176 are 1,2,4,8,16,22,44,88 and 176;
divisors of 182 are 1,2,7,13,14,26,91 and 182;
Hence, 176 as the most number of divisors.
Correct Option: C
Answer: C
Question: A man takes 5 hours 45 min. In walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is :
Options:
A)11 hrs 45 min
B)3 hrs 45 min
C)7 hrs 30 min
D)7 hrs 45 min
E)None
Rationale: Sol.
Let the distance be x km. Then,
(time taken to walk x km) + (Time taken to ride x km) = 23/4 hrs.
⇔ (Time taken to walk 2x km) + (Tie taken to ride 2x km) = 23/2 hrs.
But, time taken to ride 2x km = 15/4 hrs. ∴ Time taken to walk 2x km [23/2 - 15/4] hrs = 31/4 hrs = 7 hrs 45 min.
Answer A
Answer: A
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
Options:
A)30
B)40
C)50
D)60
E)80
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
B)
Answer: B
Question: Given that 268x74= 19332, find the value of 2.68x.74.
Options:
A)1.9332
B)1.0025
C)1.5693
D)1.0266
E)None
Rationale: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9332
Answer A
Answer: A
Question: After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6700. Find the actual price of the good.
Options:
A)s. 6000
B)s. 9000
C)s. 10800
D)s. 9795
E)s. 9980
Rationale: Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6700
1 = 6700/68.4
100 = (6700*100)/68.4 = Rs. 9795.
Answer: Option D
Answer: D
Question: The sum and product of two numbers are 12 and 35 respectively. The sum of their reciprocals is
Options:
A)12/35
B)1/35
C)35/8
D)35/9
E)1/45
Rationale: X + Y = 12
XY = 35
1/X + 1/Y = (X + Y)/Xy = 12/35
Answer A.
Answer: A
Question: Given f(x) = 2x – 3, for what value of x does 2*[f(x)] – 11 = f(x – 2) ?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 2(2x-3)-11 = 2(x-2) - 3
2x = 10
x = 5
The answer is D.
Answer: D
Question: The speed of a boat in still water in 20 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is:
Options:
A)9.6
B)10.2
C)9.2
D)10.4
E)9.0
Rationale: Speed downstream = (20 + 3) = 23 kmph
Time = 24 minutes =24/60 hour = 2/5 hour
Distance travelled = Time × speed =2/5×23= 9.20 km
Answer is C.
Answer: C
Question: A bag contains seven white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Options:
A)25/28
B)28/55
C)25/26
D)25/23
E)25/14
Rationale: Two balls can be picked from eleven balls in 11Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµ ways.
The required probability = (7 * 4) = 28/55 = 28/55
Answer: B
Answer: B
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3960. What is the difference between Rohan’s and Sudhir’s share in the profit?
Options:
A)s.345
B)s.350
C)s.352
D)s.360
E)s.368
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3960 × 1/11 = Rs.360.
D
Answer: D
Question: If k^2 = m^2, which of the following must be not true or false?
Options:
A)k = m
B)k = −m
C)k = |m|
D)k = −|m|
E)A,B,C,D FALSE
Rationale: Since k^2=m^2 we have 0=k^2 – m^2 =(k-m)*(k+m). So k=m or k=-m.
So only (A) and only (B) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (D) tells us that k should be less than or equal to 0.
So neither (C) nor (D) cannot be the answer.
The answer is, therefore, (E).
Answer: E
Question: There are 200 rats in Rat-City. Out of the 200, 70 are street rats and the rest are domestic rats. 110 rats are gray, 30 out of the gray cats are NOT domestic ones. How many domestic rats are there which are not gray in Rat-City?
Options:
A)90
B)50
C)60
D)40
E)25
Rationale: SR=70,DR=130
GR=110,NGR=90
So SR,GR30 and DR,GR=80 NGR,SC=40 and NGR,DC=50
SR=stray rats
DR=domesticated rats
GR=Gray rats
NGR=Non Gray rats
Answer is B)
Answer: B
Question: The editor of an anthology of short stories has to select authors from a pool of 12 authors, of which 4 are female. If the anthology is to include the work of 8 authors of which at least 2 must be female, in how many ways can the editor select the authors?
Options:
A)168
B)201
C)294
D)462
E)495
Rationale: we have total 12 authors. we need to select 8. we have 8 males and 4 females.
we need to select in a such way, that at least 2 females are selected.
my first step:
12C8 = 495.
since this is a total number of combinations that we can have, regardless of the restrictions, we can eliminate right away A, B, C, and E.
why A, B, C - because the number of combinations when the restrictions are not respected is way smaller than the number of combinations in which the restrictions are respected.
nevertheless, I wanted to check further, so that to make sure I get the right answer:
second step, to get "at least 2 females", we need to deduct from 495 number of combinations when we have 8 males 0 females and when we have 7 males and 1 female.
8 males 7 females:
8C8 * 4C0 = 8
7 males and 1 female: 8C7*4C1=32.
Thus, the required number of combinations = Total - case with 0 females - case with 1 female = 495-1-32=462.
D is the correct answer.
Answer: D
Question: Line Q has the equation 3x + y = 7. Which of the following lines is perpendicular to Line Q?
Options:
A) y = 3x + 4
B) y = –3x – 6
C) y = (1/3)x – 1
D) y = (–1/3)x + 2
E) y = (–7/3)x – 5
Rationale: I first rewrote the equation in the standard y=mx+b form. Therefore, Line Q as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line Q? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
Answer: C
Question: 0.01 is what percent of 0.1?
Options:
A)1%
B)10%
C)100%
D)50%
E)25%
Rationale: Required percentage = 0.01*100/0.1 = 100/10 = 10%
Answer is B
Answer: B
Question: if 5 a = 3125, then the value of 5(a-3) is :
Options:
A)25
B)125
C)625
D)1625
E)None of these
Rationale: Solution
5 a = 3125 ⇔ 5 a = 5 a ⇔ a = 5.
∴ 5(a - 3) = 5(5 - 3) = 52 = 25.
Answer A
Answer: A
Question: The average (arithmetic mean)T of the four distinct positive integers p, q, s and t is x. If p and q are odd, and s and t are even, which of the following must be true?
I. x is an integer
II. (x−0.5) is an integer.
III. 2x is an odd integer.
Options:
A)I only
B)II only
C)III only
D)II and III only
E)None of the above
Rationale: Given :
p + q = EVEN (odd + odd = even)
p + q + s + t = EVEN (even + even = even) nothing more....
(p + q + s + t) / 4 = x
I.
x may or may not be integer, we only know sum of 4 variables is even not necessarily multiple of 4. I is out.
II.
Similarly, x an integer if sum of 4 variables is multiple of 4 but not an integer if it is not multiple of 4, we only know it is even. II is out.
III.
As in II, if X is integer 2x is Even, if X has decimal part (a.5), 2x is odd. III is out.
Answer E, None.
Answer: E
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
Options:
A)378
B)277
C)299
D)646
E)261
Rationale: 840 = P [1 + (10*3)/100]
P = 646
Answer: D
Answer: D
Question: If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 4?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: I get 5/8 as well
1 to 96 inclusive means we have 48 odd and 48 even integers
E O E / 4 = Integer, therefore we have 48 / 96 numbers divisible by 8
O E O / 4 = Not Integer
We cannot forget multiples of 8 from 1 to 96
We have 24 numbers that are multiple of 4
Therefore, 48/96 + 24/96 = 72/96 = 3/4
answer : E
Answer: E
Question: A train is 360 meter long is running at a speed of 56 km/hour. In what time will it pass a bridge of 140 meter length.
Options:
A)20.14 seconds
B)12.14 seconds
C)22.14 seconds
D)32.14 seconds
E)None of these
Rationale: Explanation:
Speed = 56 Km/hr = 56*(5/18) m/sec
= 140/9 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500/140/9=32.14 seconds
Answer: D
Answer: D
Question: If the sum of a number and its square is 132, then what is the number?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Explanation:
Let the number be x. Then,
x2 + x = 132
=> x2 + x - 132 = 0
=> (x + 12)(x - 11) = 0
=> x = 11
Answer: Option B
Answer: B
Question: . How many shots of 1cm radius can be prepared from a sphere of 3cm radius?
Options:
A)20
B)72
C)27
D)83
E)83
Rationale: Explanation:
4/3 π * 3 * 3 * 3 = 4/3 π * 1 * 1 * 1 * x
x = 27
Answer: Option C
Answer: C