divelab/Sys2Bench huggingface dataset:
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Sunday
E)Friday
Rationale: Explanation:
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
Answer: B
Answer: B
Question: If 40 per cent of a number is added to an other number then it becomes 125 per cent of itself. What will be the ratio of first and second numbers?
Options:
A)8 : 5
B)5 : 7
C)5 : 8
D)Data inadequate
E)None of these
Rationale: 40x⁄100 + y = 125x⁄100 ⇒ x⁄y = 20⁄17
Answer E
Answer: E
Question: Two vehicles A and B leave from Y to X. A overtakes B at 10:30 am and reaches X at 12:00. It waits for two hours and returns to Y. On its way, it meets B at 3 PM and reaches Y at 5 PM. B reaches city X waits for 1 hour and returns to y After how many hours will B reach to Y from the time A overtook him.
Options:
A)40.5
B)41.5
C)42.5
D)43.5
E)44.5
Rationale: Let the distance between City X and Y be D
As given - B leaves City X at 2:00 (12:00 + 2 hrs halt) and reaches City Y at 5:00
So it takes him 3 hours to cover distance D.
Now, A overtakes B at 10:30 and reaches city Y at 12:00 pm , which means that A traveled for 1:30 hr.
Now see,
A takes 3 hrs takes to cover distance D
so in 1.5 hrs A will cover D / 2 distance
Now see another part -
"On its way, it meets B at 3 PM and reaches Y at 5 PM."
Given that - B leaves City Y at 2 PM
So distance covered by A in 1 hr (3 - 2) = D / 3
Now Total Distance covered by B during (A overtaking B + A wait for two hour + A on its way back ) is
D / 2 [when they first overtake] - D / 3 [when they again overtake]
= D / 6
Now Time elapsed during this period (A overtaking B + A wait for two hour + A on its way back )
=1.5 + 2 + 1
=4.5
so to cover D / 6 distance B took 4.5 hr
to cover D distance B will take (4.5 * 6)
= 27 hr.
Now "After how many hours will B reach to Y from the time A overtook him."
Time to reach X after A overtook (D / 2) + wait + Time to reach Y from X (D)
= 13.5 + 1 + 27
= 41.5
ANSWER:B
Answer: B
Question: By selling 22 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)83
B)63
C)53
D)33
E)13
Rationale: 80% --- 22
120% --- ?
80/120 * 22 = 33
Answer:D
Answer: D
Question: In a group of 100 people,60 like volleyball,50 like hockey. How many like both volleyball and hockey?
Options:
A)20
B)15
C)10
D)5
E)25
Rationale: Make a Venn diagram, and enter your data.
Let the number of people who like both volleyball and hockey be x
60-x+x+50-x = 100
x = 10
so number who like both volleyball and hockey = 10
Answer C
Answer: C
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 160 marks, the no of questions he attempts correctly is :
Options:
A)35
B)38
C)40
D)42
E)44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 160
=> 5x = 220
=> x = 44
Answer: E
Answer: E
Question: A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Options:
A)3
B)5
C)6
D)4
E)9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 20 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B
Answer: B
Question: Jim covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
Options:
A)15 Kmph
B)18 Kmph
C)19 Kmph
D)20 Kmph
E)21 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
A)
Answer: A
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 17. The larger of the two numbers is:
Options:
A)276
B)299
C)391
D)345
E)354
Rationale: Clearly, the numbers are (23 x 13) and (23 x 17).
Larger number = (23 x 17) = 391.
Answer: Option C
Answer: C
Question: If 25% of a number is subtracted from a second number the second number reduces to its five-sixths. What is the ratio between the first number and the second number?
Options:
A)2 : 3
B)3 : 2
C)1 : 3
D)Data inadequate
E)None of these
Rationale: Let the first and second number be x and y respectively.
x - y × 25⁄100 = y × 5⁄6
or, y - x⁄4 = 5⁄6y
or, 1⁄6y = x⁄4y
\ x : y = 2 : 3
Answer A
Answer: A
Question: There are c cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
Options:
A)c(c-1)
B)n(n+1)
C)n(n-1)/2
D)n(n+1)/2
E)n2
Rationale: First of all, the possible number of airlines is c. Then, the possible number of airlines departing from one city to another becomes (c-1). Hence, the answer is c(c-1), A
Answer: A
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 20%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
Options:
A)20%
B)25%
C)33.33%
D)40%
E)35%
Rationale: Say 100g pure butter costs $100
But; $100 is his 25% profit because he just used 80gram pure butter.
80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.20(75)
so;
total weight=100g
fat=20g
25%
B
Answer: B
Question: The work done by a man, a woman and a child is in the ratio of 3:2:1. There are 20 men, 30 women & 48 children in a factory. Their weekly wages amount to Rs.840, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women & 30 children for 2 weeks?
Options:
A)Rs.1000
B)Rs.1050
C)Rs.1170
D)Rs.1900
E)Rs.1230
Rationale: sax Ratio of wages of 20 men, 30 women
and 45 chﬂdren perweek
: (3 x 2o):(2 x 30) (1 x 43) 5
Total wages or 20 men per week
= R5 300
Therefore, wages of a man per week : Rs 15,
sirmlarly, wages of woman per week
: Rs 10 and wages ofchwld perweek Rs 5
Total wages of (15 men, 21 women and 30
chﬂdrenj perweek
= 15x15 + 21x10 + 30x5 = 585
Total wages for 2 weeks = Rs.1170
C
Answer: C
Question: 5^100 is divided by 18. Then what is the remainder?
Options:
A)10
B)11
C)13
D)15
E)19
Rationale: Here N = 18=2×32
ϕ(18)=18(1−12)(1−13) = 6
So 56 when divided by 18, remainder is 1.
So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49
Now 49 when divided by 18, remainder is 13.
C
Answer: C
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $920 in total compensation, how many total hours did he work that week?
Options:
A)36
B)50
C)44
D)48
E)52
Rationale: For 40 hrs = 40*16=640
Excess = 920-640=280
For extra hours =.75(16)=12+16=28
Number of extra hrs =280/28=10
Total hrs =40+10=50
Answer B 50
Answer: B
Question: The bankerâ€™s gain on a sum due 3 years hence at 10% per annum is Rs. 120. The bankerâ€™s discount is
Options:
A)Rs.960
B)Rs.840
C)Rs.520
D)Rs.760
E)None
Rationale: Solution
T.D	=(B.G x 100 / R x T)
= Rs.(120x100/10 x 3)
= Rs.400.
B.D
=Rs(400+ 120)
= Rs.520.
Answer C
Answer: C
Question: Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 610 or over 780. If the individual ranges of the three people's scores in those 4 practice tests were 50, 80 and 90, what is the difference between the maximum and minimum possible ranges of all their scores put together.
Options:
A)70
B)80
C)90
D)100
E)110
Rationale: According to the information in the question the maximum range would be between 610 and 780(170). The minimum range would be the greatest range for any one individual, which is listed in the problem as 90. So the difference between these would be 170-90 or 80.
Answer: B
Answer: B
Question: Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 8 more than the average expenditure of all the nine. The total money spent by all of them was
Options:
A)36
B)40
C)29.25
D)27
E)None of the above
Rationale: Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 8 = 9x
⇒ x = 4
∴ Total money spent = 9x = 9 × 4 = 36
Answer A
Answer: A
Question: At 12:00 a.m., Tom begins traveling on a certain bike path from Riverdale at a constant rate of 10 mph. If, at 3:00 p.m., Jim begins traveling from Riverdale on the same path at a constant rate of 20 mph, at what time will he catch up to Peter?
Options:
A)5:00 p.m.
B)6:00 p.m.
C)7:00 p.m.
D)8:00 p.m.
E)9:00 p.m.
Rationale: By the time Jim starts, Tom has already covered = 3 hr * 10 mph = 30 miles
Relative speed = 20- 10 = 10mph
To catch up, Jim needs to cover 30 miles which can be covered in = 30/10= 3hours
If Jim leaves at 3 pm, he will catch Tom at 6 pm
Answer: B
Answer: B
Question: In a certain province in France there are 19 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
Options:
A)30
B)105
C)330
D)143
E)171
Rationale: 1 city needs 18 roads to connect directly to the rest => 19 city needs 19*18 roads.
One road is counted twice => the number of road needed is 19*18/2 = 171
Answer E
Answer: E
Question: The difference between C.I. and S.I. on an amount of $10,000 for 2 years is $49. What is the rate of interest per annum?
Options:
A)5%
B)6%
C)7%
D)8%
E)9%
Rationale: $49 is the interest on the first year of interest.
Let x be the interest rate.
The interest after the first year is 10000*x.
The interest on the first year's interest is 10000*x*x
10000*x^2 = 49
x = 0.07
The answer is C.
Answer: C
Question: 75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 32% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?
Options:
A)20%
B)30%
C)50%
D)55%
E)75%
Rationale: Let x be the number of non-smoking rooms.
Let N be the total number of rooms at the inn.
40% of non-smoking rooms have a king-sized bed.
0.4x = 0.32N
x = 0.8N
The percentage of rooms which permit smoking is 1 - 0.8 = 20%
The answer is A.
Answer: A
Question: A single discount equivalent to the discount series of 30%, 10% and 5% is?
Options:
A)31.5
B)31.8
C)40.1
D)31.3
E)31.1
Rationale: 100*(70/100)*(90/100)*(95/100)
= 59.9
100 - 59.9 = 40.1
Answer:C
Answer: C
Question: A table is bought for Rs.800/- and sold at a loss of 10% find its selling price
Options:
A)s.500/-
B)s.530/-
C)s.540/-
D)s.600/-
E)s.720/-
Rationale: 100 % ------> 800 (100 * 8 = 800)
90 % ------> 720 (90 * 8 = 720)
Selling price = Rs.720/-
E
Answer: E
Question: A merchant marks his goods up by 40% and then offers a discount of 15% on the marked price. What % profit does the merchant make after the discount?
Options:
A)21%
B)25%
C)69%
D)31%
E)19%
Rationale: Let the original price be 100.
After 40% markup, price = 140
After 15% discount on this marked-up price, price = 140 - (15% of 140) = 140 - 21 = 119
Final profit = ((119-100) / 100) * 100 = 19%
Option E
Answer: E
Question: A completes a work in 6 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be
Options:
A)8 days
B)9 days
C)10 days
D)4.8 days
E)13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 6 × 24/ 30 = 4.8 days.
D
Answer: D
Question: A man swims downstream 40 km and upstream 30 km taking 5 hours each time, what is the speed of the man in still water?
Options:
A)12
B)8
C)36
D)5
E)7
Rationale: 40 --- 5 DS = 8
? ---- 1
30 ---- 5 US = 6
? ---- 1 M = ?
M = (8 + 6)/2 = 7
Answer: E
Answer: E
Question: How many total number of ways in which a distinct objects can be put into two different boxes is
Options:
A)n2
B)2a
C)2n
D)3n
E)None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the a objects. So, the total number of ways is
2 × 2 ×.....× 2 (a times ) = 2a
Answer B
Answer: B
Question: An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 20% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
Options:
A)119.45%
B)129.56%
C)138.24%
D)141.92%
E)145.36%
Rationale: 0.8*1.2^3 = 1.3824
The answer is C.
Answer: C
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Options:
A)10
B)12
C)14
D)13
E)16
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: D
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 30 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
Options:
A)22 %
B)30%
C)42 6/7%
D)70%
E)130%
Rationale: Expensive item = $100;
Cheap item = $70;
We must increase $70 to $100, so by $30, which is approximately 40% increase: (100-70)/70 = 3/7 = ~0.42.
Answer: C.
Answer: C
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Options:
A)18:11
B)18:16
C)18:17
D)18:18
E)18:12
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer:A
Answer: A
Question: Find a sum for first 3 prime number'ss?
Options:
A)25
B)10
C)15
D)12
E)36
Rationale: Required sum = (2 + 3 + 5) = 10
Note: 1 is not a prime number
Option B
Answer: B
Question: Father is aged square times more than his son john. After 3 years, he would be three times of John's age. what would be the age of John's Father after 15 years ?
Options:
A)18
B)36
C)40
D)57
E)45
Rationale: Let Father's age be J and John's' age be D...
Given J + 3 = 3(D + 3 ) => J - 6 = 3D -> Eq1.
Given J-6 = (D-6)^2 --> Eq 2..
sub J-6 value in eq 2... 3D = D^2 - 12D + 36.
0 = D^2 - 15D + 36 => D = 12 or D = 3.
When D = 12 we get from eq 1... J+3 = 45 => J =42..
When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15...
In the above options only 42 exits..
IMO option D is correct answer..
Answer: D
Question: An outlet pipe can empty 2/3 of a cistern in 16 minutes. In 8 minutes, what part of the cistern will be emptied?
Options:
A)1/2
B)1/3
C)1/4
D)2/5
E)3/10
Rationale: 8/16 * 2/3 = 1/3
The answer is B.
Answer: B
Question: What is the probability that a 4-person committee chosen at random from a group consisting of 6 men, 7 women, and 5 children contains at least 1 woman?
Options:
A)11/102
B)77/204
C)77/102
D)91/102
E)31/34
Rationale: Total Members = 6+7+5 = 18
Total ways of making 4 person committee = 18C4 = 3060
Total Members without women = 6+5 = 11
Total ways of choosing e person committee without any women = (6+5)C4 = 330
favorable probability = 1- (330/3060) = 1- (11/102) = 91/102
Answer: option D
Answer: D
Question: The sum of two numbers is 30 and their difference is 10. Find their product.
Options:
A)104
B)108
C)114
D)325
E)200
Rationale: Sol.
Let the numbers be x and y.
Then, x + y = 30 and
x - y = 10
2x = 40 +> x =20 , so y = 10
x y = 20*10 = 200
Answer : E
Answer: E
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 8 minutes earlier. How far is the office from his house?
Options:
A)4 1/5 Km
B)4 1/7 Km
C)3 1/5 Km
D)3 1/7 Km
E)3 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 16/6
= 24/2 * 16/60
= 8 * 2/5
= 16/5 = 3 1/5 Km
C)
Answer: C
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Options:
A)45%
B)49%
C)57%
D)59%
E)61%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: C
Question: A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.400, find the number of 10 paise coins ?
Options:
A)914
B)714
C)718
D)724
E)814
Rationale: 50*3k + 20*4k + 10*5k = 40000
280k = 40000 => k = 142.85
50p coins = 3k = 3*142.85 = 428
20p coins = 4k = 4*142.85 = 571
10p coins = 5k = 5*142.85 = 714
ANSWER:B
Answer: B
Question: The decimal d is formed by writing in succession all the positive, even integers in increasing order after the decimal point; that is d = 0.246810121416...
What is the 100th digit of d to the right of decimal point?
Options:
A)6
B)1
C)0
D)2
E)8
Rationale: One-digit even numbers: There are (1)(10/2) = 4 even one-digit numbers.
0.2468
4 digits down, 96 remaining. The next 5 even numbers will be 10, 12, 14, 16, and 18, ... so it follows that: (2)(5) = 10 digits.
Two-digit numbers: 90 digits, which brings us to the number 98.
Three-digit numbers: we only need 6 more digits. The next even numbers are 100, and 102, thus 2 is the 100th digit.
Answer: D
Answer: D
Question: The length of the bridge, which a train 120 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)255
B)267
C)255
D)277
E)211
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec
Time = 30 sec
Let the length of bridge be x metres.
Then, (120 + x)/30 = 25/2
=> x = 255 m. Answer:C
Answer: C
Question: The speed of a boat in still water is 65kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)22 kmph
B)40 kmph
C)78 kmph
D)15 kmph
E)45 kmph
Rationale: Speed downstream = 65 + 20 = 85 kmph
Speed upstream = 65 - 20= 45 kmph
Answer:E
Answer: E
Question: Two motor cycles were sold for Rs 9,900 each, gaining 10% on one and losing 10% on the other. The gain or loss per cent in the whole transaction is
Options:
A)Neither loss nor gain
B)1% profit
C)100/99 % profit
D)1% loss
E)None of these
Rationale: C.P. of the 1st Motor Cycle = (9900 x 100)/(100 + 10) = Rs 9000
C.P. Of the 2nd Motor Cycle = (9900 x 100)/(100 - 10) = Rs 11000
Total C.P = Rs 20,000
Total S.P = Rs 19,800
Therefore, Loss per cent = (200/20000) x 100 = 1
ANSWER:D
Answer: D
Question: A sales representative receives a salary of $150 per week and earns a commission of 15% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?
Options:
A)$3,000
B)$3,150
C)$4,000
D)$4,150
E)$5,000
Rationale: Total salary = $150+ 15% (x) where x = all the sales she makes.
How much x should be for total to be 600
$150+15%(x) = $600
15%(x) = $450
x = $3000
Answer :A
Answer: A
Question: A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 30 days, then together ,all will finish the work in :
Options:
A)13 1/3 days
B)12 1/3 days
C)15 days
D)12 days
E)30 days
Rationale: C alone can finish the work in 30 days.
(A + B)can do it in 20 days
(A + B)s 1 days wok = 1/20.
As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.
Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30
(A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/30) = 1/12
All the three together will finish it in 1/12 = 12 days.
ANSWER:D
Answer: D
Question: Merry invested Rs. 8000 in a scheme for 3 years at compound interest rate 7% p.a. How much amount will Merry get on maturity of the fixed deposit?
Options:
A)s.8980
B)s.9800.34
C)s.9841
D)s.8900
E)s.8820
Rationale: Amount = [8000 * (1 + 7/100)3]
= 8000 * 107/100 * 107/100 * 107/100
= Rs.9800.34
Answer:B
Answer: B
Question: The number 4 is the smallest positive
integer that has exactly three factors:
1, 2, and 4. If k is the next-highest integer
that also has exactly three factors, what is
the sum of the three factors of k?
Options:
A)13
B)14
C)16
D)18
E)20
Rationale: The greatest of the five possible answers is 20, so k is less than 20. Use trial and error to
find the value of k:
Factors of 5: 1 5
Factors of 6: 1 2 3 6
Factors of 7: 1 7
Factors of 8: 1 2 4 8
Factors of 9: 1 3 9
Thus, k = 9, and the sum of the factors of k is 1 + 3 + 9 = 13.
correct answer A)13
Answer: A
Question: A 15 lt mixture contains water with 20% of alcohol.If 5 more lts of water added to the mixture what is the percentage of alcohol?
Options:
A)10%
B)15%
C)20%
D)25%
E)30%
Rationale: Initially the mixture contains 20% of 15=15*(20/100)=3 lts of alcohol
after mixing another 5 lts of water...
the total liquid is 20 lts..
so alcohol percentage=(3/20)*100=15%
ANSWER:B
Answer: B
Question: Two pipes can fill a tank in 12 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
Options:
A)5.5 Hours
B)7.5 Hours
C)8.5 Hours
D)9.5 Hours
E)6.5 Hours
Rationale: In 1 hour it fill 1/12 + 1/12 - 1/20 = 7/60
So fill tank fillup in 60/7 = 8.5 Hours
ANSWER:C
Answer: C
Question: A set of 17 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Options:
A)32
B)37
C)40
D)45
E)50
Rationale: The correct answer is D.
A set of 17 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Given 15 different integers, lets say
n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15
Also given median is 25 i.e. n8 = 27
n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15
Also given the range is 25 i.e. n15 - n1 (18) = 27
The maximum value n15 can have is 27 + n1 (18) = 45
D
Answer: D
Question: P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 140 days, in how many days can R alone complete the remaining work?
Options:
A)50 days
B)102.7 days
C)100 days
D)150 days
E)80 days
Rationale: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days
P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 390 days
P works for 60 days--> 60/200 work done => 30%
Q works for 140 days--> 140/250 work done => 56%
260% work left ... R alone will take 26% * 395 = 102.7 days
Answer is (B)
Answer: B
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of b - a ?
Options:
A)-10
B)10
C)-19
D)20
E)21
Rationale: Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
B - A = 100 - 110 = -10
Ans :A
Answer: A