divelab/Sys2Bench huggingface dataset:
Question: On a partly rainy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?
Options:
A)1/7
B)1/4
C)1/3
D)1/2
E)1
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is 2/14 = 1/7. Answer: A
Answer: A
Question: If a mixture is 2⁄7 alcohol by volume and 3⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
Options:
A)3
B)1/3
C)2/3
D)3/5
E)4/5
Rationale: Should be a sub-600 level Q..
volume= {2/7}/{3/7}=2/3
C
Answer: C
Question: A cyclist covers a distance of 750 meter in 3 minutes 30 seconds. What is the speed in km/hr of cyclist
Options:
A)16 km/hr
B)17 km/hr
C)18 km/hr
D)19 km/hr
E)135 km/hr
Rationale: Explanation:
Speed=Distance/Time
Distance=750meter
Time=3 min 30sec=210sec
Speed=750/210=37.5m/sec
=>37.5âˆ—18/5km/hr=135km/hr
Option E
Answer: E
Question: How many four-digit numbers that do not contain the digits 2, 3, 4, 5, 6, or 7 are there?
Options:
A)168
B)176
C)184
D)192
E)200
Rationale: The 1st digit can be filled up by the numbers: {1,8,9} = 3 ways
The 2nd digit can be filled up by the numbers: {0,1,8,9} = 4 ways
The 3rd digit can be filled up by the numbers: {0,1,8,9} = 4 ways
The 4th digit can be filled up by the numbers: {0,1,8,9} = 4 ways
The total number of such four-digit numbers is 3*4*4*4 = 192
The answer is D.
Answer: D
Question: A, B and C enter into a partnership. They invest Rs. 50,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years?
Options:
A)12 : 3 : 4
B)13 : 2 : 4
C)13: 2 : 1
D)15: 16 : 28
E)none
Rationale: Sol.
A : B : C = (50000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =180 : 192 : 336 = 15: 16 : 28
Answer D
Answer: D
Question: What is the leastvalue of x. So that 23x57 is divisible by 3?
Options:
A)3
B)4
C)1
D)5
E)6
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 7 = 17 + x
Least value of x may be 1
Therefore 17 + 1 = 18 is divisible by 3.
C
Answer: C
Question: If |4x+14| = 46, what is the sum of all the possible values of x?
Options:
A)2
B)-7
C)4
D)-5
E)6
Rationale: There will be two cases
4x+14= 46 or 4x+14 = -46
=> x =8 or x= -15
sum of both the values will be -15 +8 = -7
Answer is B
Answer: B
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
A)288
B)270
C)287
D)209
E)271
Rationale: I = (500*9*6)/100 = 270
Answer: B
Answer: B
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Options:
A)22
B)20
C)99
D)77
E)655
Rationale: x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Answer:B
Answer: B
Question: A box contains ten light out of which 5 are defective. If five light are chosen at random, find the probability that all the five light are defective?
Options:
A)2/523
B)3/253
C)5/126
D)3/252
E)1/252
Rationale: Out of nine light , five are good and four are defective.
Required probability = 5C5/10C5 = 1/252
E
Answer: E
Question: 11 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?
Options:
A)80
B)160
C)720
D)1100
E)1540
Rationale: No. of ways of picking 2 biology books(from 11 books) = 11c2 = (11*10)/2 = 55
No. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28
Total ways of picking 2 books of each type = 55*28 =1540
(Option E)
Answer: E
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?
Options:
A)6 km
B)3 km
C)7 km
D)9 km
E)2 km
Rationale: Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 47/60
47x/60 = 47/60 => x = 1.
Total distance = 3 * 1 = 3 km.
Answer:B
Answer: B
Question: Look at this series: -2, 0, 2, 4,... What number should come next?
Options:
A)6
B)12
C)8
D)9
E)10
Rationale: Explanation: This is a simple addition series; each number is added by 2 to the previous number. In other terms to say, the number is added by 2 successively to get the next result.
-4+2 = -2
-2+2 = 0
0+2 = 2
2+2 = 4
4+2 = 6 and so on.
Answer: Option A
Answer: A
Question: Dhoni decides to attend a tennis game with four friends. If the party of five sits together in five consecutive seats, and Dhoni must NOT sit in between two of his friends, how many ways can the five friends be arranged?
Options:
A)6
B)48
C)36
D)24
E)12
Rationale: Dhoni have to sit at either of the ends.
If Dhoni sits on the left most corner, then other 5 friends can be arranged in 4! = 24
David can also sit on the other end, then another 4! ways we can arrange.
So total number of ways = 24+24 = 48
Answer : B
Answer: B
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 40% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 20% Vermouth by volume. How many ounces of Gin must he add?
Options:
A)n/6
B)n/3
C)3n/5
D)5n/6
E)8n/5
Rationale: 4 ounces is vermouth
6 ounces of gin...
Total volume 10.
To make vermouth account for 20% of total volume the new volume must be....
x*0.2=4
x=20 ounces....
So now you see that he must add 10 ounces of gin...
Plug in 12 for n in the answer choices and look for answer 10
D
Answer: D
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.90 less, he could have gained 25%. What is the cost price?
Options:
A)372
B)375
C)278
D)267
E)450
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
90 ----- ? => 450
Answer:E
Answer: E
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.1,50,000 earned at the end of 3 years from the start of the business in 1999?
Options:
A)Rs 45000
B)Rs 50000
C)Rs 70000
D)Rs 75000
E)None
Rationale: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(150000×2/6) = Rs.50000.
Answer B
Answer: B
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 5 games?
Options:
A)x + 3y/(n + 3)
B)x + y/(n + 3)
C)(x + 3y)/(n + 3)
D)(nx + 3y)/(n + 5)
E)(3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 5 games = (nx+3y)/(n+5)
Hence, correct answer will be (D)
Answer: D
Question: How many 4-digit no's that are divisible by 10 can be formed from the no.'s 3, 5, 7, 8, 9, 0 such that no no. repeats?
Options:
A)20
B)30
C)60
D)70
E)90
Rationale: If a number is divisible by 10, its units place should contain a 0.
_ _ _ 0
After 0 is placed in the units place, the tens place can be filled with any of the other 5 digits.
Selecting one digit out of 5 digits can be done in 5C1 = 5 ways.
After filling the tens place, we are left with 4 digits. Selecting 1 digit out of 4 digits can be done in 4C1 = 4 ways.
After filling the hundreds place, the thousands place can be filled in 3C1 = 3 ways.
Therefore, the total combinations possible = 5*4*3 = 60.
C
Answer: C
Question: The "Racing magic" takes 120 seconds to circle the racing track once. The "Charging bull" makes 40 rounds of the track in an hour. If they left the starting point together, how many minutes will it take for them to meet at the starting point for the second time?
Options:
A)3
B)6
C)9
D)12
E)15
Rationale: Time taken by Racing magic to make one circle = 120 seconds = 2 mins
Time taken by "Charging bull" to make one circle = 60 mins / 40 = 1.5 mins = 90 seconds
LCM of 90 and 120 seconds = 360 seconds = 6 mins
Time taken for them to meet at the starting point for the second time = 6 mins *2 = 12 mins
Answer D
Answer: D
Question: Find value of x
(11^2 + 12^2 + 13^2 + ... + 20^2) = x
Options:
A)1200
B)1340
C)1234
D)1203
E)2485
Rationale: (11^2 + 12^2 + 13^2 + ... + 20^2) = (1^2 + 2^2 + 3^2 + ... + 20^2) - (1^2 + 2^2 + 3^2 + ... + 10^2)
6
= 20 x 21 x 41	-	10 x 11 x 21
6	6
= (2870 - 385)
= 2485
E
Answer: E
Question: A certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts, by weight. What is the number of pounds of almonds in 350 pounds of the mixture ?
Options:
A) 250
B) 84
C) 40
D) 28
E) 20
Rationale: Almonds : Walnuts = 5 : 2
Total mixture has 7 parts
In a 350 pound mixture, Almonds are 5/7 (total mixture)
= 5/7 * 350 = 250 pounds
Answer (A)
Answer: A
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $90 to incur a loss 20%?
Options:
A)45
B)36
C)40
D)50
E)48
Rationale: Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $90*(100% + 20%) = $108
Number of articles to be sold for $108 to incur a 20% loss: $108 / $2.40 = 45
Thus, solution A is correct.
Answer: A
Question: Two vessels contains equal number of mixtures milk and water in the ratio 5:2 and 6:1. Both the mixtures are now mixed thoroughly. Find the ratio of milk to water in the new mixture so obtained?
Options:
A)1:3
B)9:13
C)5:11
D)11:3
E)15:4
Rationale: The ratio of milk and water in the new vessel is = (5/7 + 6/7) : (2/7 + 1/7)
= 11/7 : 3/7 = 11:3
Answer is D
Answer: D
Question: A man can row upstream at 7 kmph and downstream at 10 kmph.Find man's rate in still water and the rate of current?
Options:
A)1.2 km/hr
B)1.5 km/hr
C)1.6 km/hr
D)1.8 km/hr
E)None
Rationale: Solution
Rate in still water	= 1 / 2 (10 + 7) km/hr
= 8.5 km/hr.
Rate of current	= 1 / 2(10 - 7) km/hr
= 1.5 km/hr.
Answer B
Answer: B
Question: The sum of two number is 25 and their difference is 13. Find their product.
Options:
A)104
B)114
C)315
D)325
E)None
Rationale: EXPLANATION
Let the numbers be x and y.
Then, x + y = 25 and x – y = 13.
4xy = (x + y)2 – (x– y)2
= (25)2 – (13)2
= (625 – 169)
= 456
xy = 114.
Answer B
Answer: B
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
Options:
A)10
B)88
C)267
D)28
E)21
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours = 10 hours.
Answer: A
Answer: A
Question: The present worth of a sum due sometimes hence is Rs.5760 and the banker's gain is Rs.10. What is the true discount?
Options:
A)Rs. 480
B)Rs. 420
C)Rs. 120
D)Rs. 240
E)Rs. 260
Rationale: Explanation:
TD = √PW × BG=√5760×10=√57600 = Rs. 240
Answer: Option D
Answer: D
Question: In an Examination there are three subject of 100 marks each. A student scores 60% in the 1st subject and 80% in the second subject. He scored 70% in aggregate. His percentage of marks in the third subject is:
Options:
A)70
B)80
C)60
D)65
E)66
Rationale: Explanation :
Let be the score of third subject = X
A student of score in first subject = 60% = 60 x 100/100 = 60
A student of score in second subject = 80% = 80 x 100/100 = 80
70% of 300 = 300 x 70/100 = 210
score of third subject = 210 – ( 60 + 80)
= 210 – 140 = 70
Percentage of score in third subject = 70 x 100/100 = 70%
Hence, the answer is 70%
Answer : A
Answer: A
Question: The arithmetic mean of the scores of a group of students in a test was 62. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
Options:
A)A)61.4.
B)B)51.7
C)C)69.54
D)D)51.1
E)E)51.2
Rationale: Let the required mean score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 62 * 100
= 1600 + 775 + 55x = 6200
= 55x = 3825
= x = 69.54
Answer:C
Answer: C
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)1/0
B)1/3
C)1/1
D)1/7
E)1/5
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer: B
Answer: B
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1240. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
Options:
A)2480
B)3490
C)6785
D)8215
E)9255
Rationale: sum of square of n numbers is found using the formula [n (n+1) (2n+1)]/6
we have sum of 1st 15 numbers = 1240
we need to find sum of squares from 16 to 30 which is = sum of squares of 1st 30 +ve integers - sum of squares of 1st 15 +ve integers.
we will get D - 8215;ANSWER:D
Answer: D
Question: Eight men, ten women and six boys together can complete a piece of work in eight days. In how many days can 20 women complete the same work if 20 men can complete it in 12 days?
Options:
A)33
B)77
C)66
D)22
E)99
Rationale: Let the number of units which can be completed by each man, each women and each boy be m/day, w/day and b/day respectively.
Work = 8(8m + 10w +6b)units = 12(20m)
10w +6b = 22m
b is unknown.
We cannot find the relation between m and w.
We cannot answer the question.
Answer:D
Answer: D
Question: Which of the following is divisible by the first five positive integer multiples of 23?
(i) 11110
(ii) 102120
(iii) 307740
Options:
A)None
B)iii only
C)i and iii only
D)ii and iii only
E)i, ii and iii
Rationale: A positive integer x is divisible by the first five integer multiples of 23 if and only if it is divisible by their least common multiple, 3*4*5*23=60*23=1380.
The sum of the integers of 11110 is 4 so 11110 is not divisible by 3, hence not divisible by 1380.
102=17*6 and 120=20*6, so 102120=60*(1700+2)=60*1702=60*2*851. Now, 851-30*23=851-690=161=7*23, so 102120 is divisibly by 60*23=1380.
Finally, 102120*3=306360, and 306360+1380=307740, so (iii) is also divisible by 1380.
Answer D.
Answer: D
Question: A local bank that has 20 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 20 codes?
Options:
A)3
B)4
C)7
D)6
E)5
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Add one more integer: 5
55, 15, 51, 25, 52, 35, 53,54,45 = 9 Codes
Total = 25 Codes. Enough.
Answer: E
Answer: E
Question: If 3/p = 6 and 3/q = 15 then p – q = ?
Options:
A)3/19
B)3/11
C)3/17
D)3/10
E)3/13
Rationale: Explanation:
3p3p = 6 , p = 3636 = 1212and
3q3q = 15 , q = 315315 = 1515 then
p – q = 1/2 – 1/5 = 3/10
Answer: D
Answer: D
Question: The cost of the paint is rs.50 per kg. if 1kg of paint covers 20 sq.ft, how much will it cost to paint outside of a cube having 20 feet each side
Options:
A)Rs.962
B)Rs.6000
C)Rs.546
D)Rs.876
E)None of these
Rationale: Explanation:
surface area of a cube= 6 x 20^2 = 2400 sq.ft
quantity of paint required=(2400/20)=120 kg
cost of painting= 50x 120= Rs.6000
Answer: B
Answer: B
Question: If the city centers of Tokyo and Rome are 6124 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)
Options:
A)1.7 × 10^7
B)4.8 × 10^7
C)3.9 × 10^8
D)2.7 × 10^9
E)1.5 × 10^10
Rationale: 6124 miles = 6124 x 5280 feet/mile x 12 inches/foot which is about 3.9 x 10^8 inches.
The answer is C.
Answer: C
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options:
A)12:15:18
B)12:15:16
C)12:15:10
D)12:15:12
E)12:15:11
Rationale: Explanation:
Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B
Answer: B
Question: The mean of 50 observations was 36. it was found later an observation 48 was wrongly taken as 23 . the corrected new means is :
Options:
A)35.2
B)36.1
C)36.5
D)39.1
E)None of these
Rationale: Solution
Correct sum = (36 × 50 + 48 - 23) = 1525.
∴ correct mean = 1825/50=36.5 Answer C
Answer: C
Question: Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 7%. What is the approximate interest he pays annually?
Options:
A)1000
B)1500
C)3000
D)2500
E)2400
Rationale: An easy way too attempt this is by approximation:
For the first quarter, he pays 7% of 10,000 which is $700.
So for the four quarters in the year, he will approximately play 700*4=2800 over the entire year.
Because of compound interest it will be more than 2800. Approx. option C is correct.
Answer : C
Answer: C
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A) 2:9
B) 2:7
C) 1:6
D) 1:4
E) 1:3
Rationale: (10/100)A+(3/100)B = (4/100)(A+B)
6A =B
=> A/B = 1/6
Answer is C.
Answer: C
Question: If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)?
Options:
A)0.36
B)0.4
C)0.42
D)0.43
E)0.64
Rationale: P(B|A) = P(A n B)/P(A)
P(A n B) = P(B|A) × P(A)
P(A n B) = 0.2 × 0.18
P(A n B) = 0.36
A
Answer: A
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 8200, then what will be the share of Sameer in the profit?
Options:
A)s.2323
B)s.2380
C)s.2800
D)s.2329
E)s.2312
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 8200 * 14/41
= Rs.2800.
Answer: C
Answer: C
Question: The difference between the local value and the face value of 7 in the numeral 32675149 is
Options:
A)69950
B)69993
C)69997
D)70000
E)01000
Rationale: (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993
B
Answer: B
Question: Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 4 fantasy books, there are 5 reference books. If the proportion of history to fantasy books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
Options:
A)6
B)21
C)24
D)32
E)36
Rationale: For every 2 history books, there are 7 fantasy books:
Originally H:F = 2:7. After the change, H:F = 4:7 = 16:28
For every 4 fantasy books, there are 5 reference books:
F:R = 4:5 = 28:35
H:F:R = 16:28:35
There are fewer than 60 fantasy books, so there are 28 or 56 fantasy books.
The number of history books could be 16 or 32.
The answer is D.
Answer: D
Question: One side of a triangle has length 9 and a second side has length 4. Which of the following could be the area of the triangle?
I. 30
II. 20
III. 10
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I, II, and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 9 and 4 are the base and height of triangle .
Area = 1/2 * 9 * 4 = 18
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 18
The answer is C.
Answer: C
Question: Calculate the L.C.M of 1/5, 6/ 7, 5/6, 3/5 is :
Options:
A)15
B)30
C)20
D)40
E)10
Rationale: Required L.C.M =L.C.M. of 1, 6, 5, 3/H.C.F. of 5, 7, 6, 5 =30/1=30
Answer is B
Answer: B
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
Options:
A)37.6
B)37.5
C)37.7
D)37.2
E)37.1
Rationale: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%.Answer: B
Answer: B
Question: If the two-digit integers F and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of F and N?
Options:
A)181
B)165
C)121
D)99
E)44
Rationale: Since the question asks for the answer that CANNOT be the sum of F and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that F and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of F and N.
Let's start with the 'easiest' answer first:
44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E
Now let's work through the rest of the list....
Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D
Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C
Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B
There's only one answer left....
A
Answer: A
Question: There is a 10% chance that Tigers will not win at all during the whole season. There is a 30% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season?
Options:
A)A)55%
B)B)60%
C)C)80%
D)D)72%
E)E)70%
Rationale: There is a 10% chance that Tigers will not win at all during the whole season
We can infer that there is 90% chance Tigers will win .
Similarly There is a 30% chance that Federer will not play at all in the whole season
We can also infer that there is 70% chance that Federer will play.
Answer E
Answer: E
Question: Solve below question 2x + 1 = -17
Options:
A)7
B)-9
C)10
D)-1
E)2
Rationale: 1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B
Answer: B
Question: To be elected president of a certain organization, a candidate needs the votes of at least 2/3 of its 1,331 members. What is the least number of votes the candidate needs to be elected?
Options:
A)443
B)444
C)887
D)888
E)889
Rationale: required votes>= 1331∗2/3
votes should be an integer, thus we can take
required votes = 1332∗2/3( because 1332/3 will be an integer )
= 888
ANSWER:D
Answer: D
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
Options:
A)148
B)150
C)152
D)158
E)160
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: D