divelab/Sys2Bench huggingface dataset:
Question: Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?
Options:
A)30
B)36
C)70
D)80
E)150
Rationale: Method I: the rates solution
“Rane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Rane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Rane + Zane is
R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:
T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36
BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Rane and Zane need 36 weeks to make 15 drums.
Answer = B.
Answer: B
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
Options:
A)2/21
B)1/21
C)3/25
D)3/29
E)8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: E
Question: 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?
Options:
A)60%
B)80%
C)50%
D)90%
E)70%
Rationale: Explanation:
Let total number of men = 100
Then
80 men are less than or equal to 50 years old
(Since 80% of the men are less than or equal to 50 years old)
=> 20 men are above 50 years old (Since we assumed total number of men as 100)20% of the men above the age of 50 play football⇒Number of men above the age of 50 who play football = 20 × 20/100 = 4
Number of men who play football = 20 (Since 20% of all men play football)
Percentage of men who play football above the age of 50 = 420 × 100 = 20%
=>Percentage of men who play football less than or equal to the age 50 = 100% − 20% = 80%
Answer: Option B
Answer: B
Question: Set A: 3, e, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – e?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: So we have even no. of elements in the Set
So median is the average of Middle two numbers
(e+8)/2= (y+9)/2
y - e= -1
Answer B
Answer: B
Question: A woman and a girl complete a work together in 24 days. If for the last 6 days woman alone does the work then it is completed in 26 days. How long the girl will take to complete the work alone?
Options:
A)days
B)days
C)days
D)days
E)days
Rationale: Explanation:
(woman + girl )’s 1 day’s work = 1/24
Their 20 day’s work = 1/24 × 20 = 5/6
The remaining 1/6 work is done by the woman in 6days
Therefore, the woman alone will finish the work in 6 × 6 days = 36 days
woMan’s 1 day’s work = 1/36
Therefore, girl 1 day’s work = 1/24 – 1/36 = 3 – 2 /72 = 1/72
Therefore, the girl alone will finish the work in 72 days.
Answer: Option A
Answer: A
Question: The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 48 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?
Options:
A)55
B)56
C)57
D)58
E)59
Rationale: 20x + 48 = 21(x – 5)
X=57
ANSWER:C
Answer: C
Question: There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of mess were increased by 42 per day while the average expenditure per head diminished by 1. What was the original expenditure of the mess?
Options:
A)400
B)420
C)445
D)465
E)None of the above
Rationale: Let the original average expenditure be `x.
Then,
42(x – 1) – 35x = 42 ⇔ 7x = 84 ⇒ x = 12.
∴ Original expenditure = (35 × 12)= 420.
Answer B
Answer: B
Question: Mike needs 30% to pass. If he scored 212 marks and falls short by 16 marks, what was the maximum marks he could have got?
Options:
A)643
B)677
C)760
D)767
E)832
Rationale: If Mike had scored 16 marks more, he could have scored 30%
Therefore, Mike required 212 + 16 = 228 marks
Let the maximum marks be m.
Then 30 % of m = 228
(30/100) × m = 228
m = (228 × 100)/30
m = 22800/30
m = 760
Answer:C
Answer: C
Question: If A is thrice as fast as B and together can do a work in 24 days. In how many days A alone can do the work?
Options:
A)36
B)42
C)28
D)32
E)45
Rationale: A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/24
= 3+1/3x = 4/3x = 1/24
x = 24*4/3 = 32
ANSWER:D
Answer: D
Question: At Joel’s bookstore, the current inventory is 30% historical fiction. Of the historical fiction books, 40% are new releases, while 50% of the other books are new releases. What fraction of all new releases are the historical fiction new releases?
Options:
A)4/25
B)12/47
C)2/5
D)8/15
E)2/3
Rationale: let there be 100 books in all
Historic fiction books = 30% of total = 30
Other books = 70
New historic fiction = 40% of 30 = 12
Other new books = 50% of 70 = 35
total new books = 35+12 = 47
fraction = 12/47
Ans: B
Answer: B
Question: In a group of Houses,40 had dogs,30 had cats and 10 houses having both dogs and cats. what is the number of houses?
Options:
A)30
B)60
C)40
D)45
E)50
Rationale: Make a Venn diagram, and enter your data.
Let the number of houses be x
30+10+20=x
x = 60
so number of houses were = 60
Answer B
Answer: B
Question: A transport company's vans each carry a maximum load of 13 tonnes. 12 sealed boxes each weighing 9 tonnes have to be transported to a factory. The number of van loads needed to do this is
Options:
A)38
B)12
C)98
D)27
E)22
Rationale: Explanation:
12 as all boxes are sealed.
Answer: B
Answer: B
Question: Look at this series: 88, 88, 78, 78, 68, 68, ... What number should come next?
Options:
A)14
B)15
C)58
D)19
E)11
Rationale: In this series, each number is repeated, then 10 is subtracted to arrive at the next number.
The next number is 58
Answer : C
Answer: C
Question: There are 13 South American countries, Anni has won a ticket to fly from Denver to one South American country and then directly to another South American Country before returning home to Denver again. Assuming there are four airports in each country, how many flights paths can Anni choose from?
Options:
A)13.12.11.10.4.4.
B)13.12.11.10.4
C)13.12.4.4.
D)13.12.4
E)13.13.13.13
Rationale: flights paths can Anni choose fromThere are 13 ways to chose the first destination,
then, 12 ways to chose next destination, with option of 4 airports (13x4)
then, to return he has 4 options to chose the airports
Thus, 13*12*4*4 ways.
Using permutations:
If the solution had written 13P1 instead of 13C1 it won't matter. As per the definition - making arrangements of the combinations gives permutations.
Since there are no arrangement for 1 item, permutationscombinations are equal.C
Answer: C
Question: If b < 3 and 3x - 3b = 0, which of the following must be true?
Options:
A)x > -3
B)x < 2
C)x = 3
D)x < 3
E)D. x > 3
Rationale: 3x - 3b = 0
Therefore, 3x = 3b
As, b<3
3x < 3(3)
i.e x < 3
Answer : D
Answer: D
Question: Bucket A is 1/4 full of sand, and Bucket B, which has one-half the capacity of Bucket A, is 3/8 full of sand. Jana pours the contents of Bucket B into Bucket A. Bucket A is now filled to what fraction of its capacity?
Options:
A)3/8
B)7/16
C)1/2
D)5/8
E)7/8
Rationale: let capapcity of a = x
sand = x/4
capacity of b = x/2
sand = 3x/16
A total = x/4 + 3x/16 = 7x/16
ANSWER:B
Answer: B
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
Options:
A)125/176
B)125/129
C)125/126
D)125/120
E)125/130
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer:C
Answer: C
Question: Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8)
Options:
A)6/k
B)8/k
C)83k
D)2/k
E)1/k
Rationale: Part of the book he can read in 1 minute = 1/k
Part of the book he can read in 8 minutes =8/k.
Answer: B
Answer: B
Question: A began business with Rs.27000 and was joined afterwards by B with Rs.36000. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)1.5
B)6.5
C)7.5
D)8
E)2
Rationale: 27*12 : 36*x = 2: 1
x = 4.5
12 -4.5 = 7.5
Answer: C
Answer: C
Question: Helen went to the stationers and bought things worth Euro 24, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)uro 16.70
B)uro 15.70
C)uro 13.70
D)uro 19.70
E)uro 18.70
Rationale: E
Euro 18.70
Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [24 - (5 + 0.30)] = Euro 18.70
Answer: E
Question: If a Ã— b = 2a - 3b + ab, then 3 Ã— 4 + 4 Ã— 3 is equal to :
Options:
A)17
B)23
C)24
D)25
E)26
Rationale: Explanation:
3 Ã— 4 + 4 Ã— 3 = (2 Ã— 3 - 3 Ã— 4 + 3 Ã— 4) + ( 2 Ã— 4 - 3 Ã— 3 + 4 Ã— 3)
= (6 + 8 - 9 + 12) = 17.
Answer: A
Answer: A
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150m
B)278m
C)286m
D)121m
E)112m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
Options:
A)15/16
B)11/16
C)11/12
D)1/2
E)5/8
Rationale: XXXX(1}{1}{1}
X can be a prime number or non prime number
Prime number:2,3,5,7
Non prime-4,6,8,9(1 is already taken)
Probability(X is a Prime number)=4/8=1/2
Probability(X is a non-prime number)=4/8=1/2
So,Atleast 2 prime numbers=P P NP NP=4!/2!2!*1/2*1/2*1/2*1/2=6/16
Three prime numbers and one Non prime=P P P NP=4!/3!*1//2^4=4/16
All prime=PPPP=1/16
Total=11/16.
Answer:B
Answer: B
Question: Which of the following could be the value of x, if |4x – 2| = 10?
Options:
A)-3
B)-2
C)1
D)2
E)4
Rationale: |4x – 2| = 10
=> 4x - 2 = 10
or 4x - 2 = -10
=> 4x = 12 or 4x = -8
=> x = 3 or x = -2
Answer B
Answer: B
Question: A boat having a length 6 m and breadth 3 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
Options:
A)100 kg
B)120 kg
C)89 Kg
D)180 Kg
E)110 Kg
Rationale: Volume of water displaced	= (6 x 3 x 0.01) m3
= 0.18 m3.
Mass of man = Volume of water displaced x Density of water
= (0.18 x 1000) kg
= 180 kg.
Answer: D
Answer: D
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Options:
A)30 min
B)20 min
C)25 min
D)40 min
E)45 min
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? 20
ANSWER B
Answer: B
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)3329
C)2776
D)2988
E)1681
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: A
Question: Twelve years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
Options:
A)A)35
B)B)34
C)C)42
D)D)25
E)E)26
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Twelve years ago, P was half of Q in age
=> 2(3x – 12) = (4x – 12)
=> 6x – 24 = 4x – 12
=> 2x = 12
=> x = 6
7x = 7*6 = 42
Answer: Option C
Answer: C
Question: The average of five consecutive odd numbers A, B, C, D and E is 25. What percent of E is C ?
Options:
A)86.2
B)87.5
C)56.8
D)88.9
E)89.9
Rationale: Explanation :
In such a case the middle number (C) is the average
∴ C = 25 and F = 29
Required percentage = 25/29 x 100 = 86.2
Answer : Option A
Answer: A
Question: The ratio 3 : 5 expressed as a percent equals
Options:
A)60%
B)40%
C)80%
D)125%
E)None
Rationale: Solution
3 : 5	= 3/ 5
= (3 / 5 x 100)%.
= 60 %.
Answer A
Answer: A
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is -
Options:
A)1/10
B)9/10
C)1/5
D)3/10
E)1/2
Rationale: Explanation:
10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
ANSWER IS C
Answer: C
Question: Two trains start at same time from two stations and proceed towards each other at the rate of 20 km/hr and 25 km/hr respectively. When they meet, it is found that one train has traveled 50 km more than the other. What is the distance between the two stations?
Options:
A)540 km
B)767 km
C)276 km
D)450 km
E)176 km
Rationale: Explanation:
Let us assume that trains meet after 'x' hours
Distance = speed * Time
Distance traveled by two trains = 20x km and 25x km resp.
As one train travels 50 km more than the other,
25x â€“ 20x =50
5x = 50
x = 10 hours
As the two trains are moving towards each other, relative speed = 20 + 25 = 45 km/hr
Therefore, total distance = 45*10 = 450 km.
ANSWER: D
Answer: D
Question: If Josh, Doug, and Brad have a total of $77 between them, and Josh has three times as much money as Brad but same as much as Doug, how much money does Doug have?
Options:
A)$8
B)$9
C)$27
D)$33
E)$36
Rationale: Josh + Doug + Brad = 77 ; Joush = 3 brad, Josh = Doug
Josh +1/3 Josh+ Josh = 77 (substituted the given values)
Josh = 33. 33=Doug =33
Answer is D.
Answer: D
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is
Options:
A)14 years
B)18 years
C)20 years
D)22 years
E)None
Rationale: Solution
Let the son's present age be x years .Then, man's present age	= (x+24)years.
Then	‹=›(x+24)+2= 2(x+2)
‹=›x+26=2x+4
x= 22.
Answer D
Answer: D
Question: 8 : 4 seconds :: ? : 4 minutes
Options:
A)10
B)8
C)20
D)25
E)30
Rationale: 8*4=4*x
x=8
ANSWER:B
Answer: B
Question: David invested certain amount in three different schemes. A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in scheme C was 150% of the amount invested in scheme A and 240% of the amount invested in scheme B, what was the amount invested in scheme B?
Options:
A)5000
B)3677
C)2977
D)2678
E)2611
Rationale: Let x, y and z be the amount invested in schemes A, B and C respectively. Then,
(x * 10 * 1)/100 + (y * 12 * 1)/100 + (z * 15 * 1)/100 = 3200
10x + 12y + 15z = 320000
Now, z = 240% of y = 12/5 y
And, z = 150% of x = 3/2 x
x = 2/3 z = ( 2/3 * 12/5) y = 8/5 y
16y + 12y + 36y = 320000
y = 5000
Sum invested in scheme B = Rs. 5000.
Answer: A
Answer: A
Question: The perimeter of a square is 48 cm. The area of a rectangle is 4 cm2 less than the area of the square. If the length of the rectangle is 14 cm, then its perimeter is
Options:
A)42
B)48
C)52
D)56
E)58
Rationale: Side of the square = 12 cm. Area of the rectangle = [(12 x 12) Ã¢â‚¬â€œ 4]
cm2 = 140 cm2
Now, area = 140 cmÂ², length = 14 cm.
Breadth = A/L = 140/14 cm. = 10 cm.
Hence, Perimeter = 2 (l + b) = 2 (14 + 10) cm = 48 cm.
Answer :B
Answer: B
Question: The LCM and HCF of two numbers are 8 and 48 respectively. If one of them is 24, Find the other ?
Options:
A)12
B)14
C)15
D)16
E)20
Rationale: HCF x LCM = Product of Numbers
8 x 48 = 24 x the other number
other number = (8 x 48) / 24
other number = 16
ANSWER : D
Answer: D
Question: In March, Kurt ran an average of 1.5 miles an hour. If by June he had increased his pace by 20 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
Options:
A)2380/60^2
B)2410/60^2
C)2390/60^2
D)3586/60
E)60^2/3590
Rationale: Kurt ran at an average of 1.5 miles/hour in march. So to run 1 mile he would take 1/1.5 hours = (60 * 60)/1.5 seconds = 2400 seconds.
If he increases his speed by 20 seconds, he will complete a mile in 2380 seconds. Converting in hours = 2380/(60 * 60) = 2380/(60^2)
ANSWER: A
Answer: A
Question: 111 = O
222 = E
333 = T
444 = S
Reading and analyzing the above, can you find out the following ?
555 = ?
Options:
A)8
B)3
C)1
D)5
E)0
Rationale: E
0
1 * 1 * 1 = One
2 * 2 * 2 = Eight
3 * 3 * 3 = Twenty seven
4 * 4 * 4 = Sixty Four
For all the above, you can see that the first letter of the sum is the code.
Thus 5 * 5 * 5 = One twenty five
Thus 555 = O.
Answer: E
Question: 8 people decided to split the restaurant bill evenly. If the bill was $214.15 dollars, how much money did they 1 cent is the smallest unit?
Options:
A)$214.16
B)$214.17
C)$214.18
D)$214.19
E)$214.20
Rationale: If the last three digits of a whole number are divisible by 8, then the entire number is divisible by 8
the last 3 digit 415 not divisible by a
Hence, we need to add 1 to this number for it to be divisible by 8
Correct Option: A
Answer: A
Question: In how many ways a committee, Consisting of 2 men and 6 women can be formed from 8 men and 10 women?
Options:
A)2660
B)5880
C)11760
D)5040
E)720
Rationale: To choose Required number of ways to form a committee:
Select 2 men out of 8 men and 6 women out of 10 women.
That is 8C2 * 10C6.
8C2=8!/2!*6!=28
10C6=10!/6!*4!
=210
The Required number of ways=210*28=5880
B
Answer: B
Question: what is the least number. which should be added to 0.0320 to make it a perfect square?
Options:
A)0.0005
B)0.0004
C)0.0006
D)0.0002
E)0.0001
Rationale: 0.0320+0.0004=0.0324
(0.18)^2
ANSWER:B
Answer: B
Question: If 16% of 40% of a number is 3, then the number is
Options:
A)200
B)225
C)46.875
D)320
E)None of these
Rationale: Explanation:
Let 16/100×40/100×a=3
a = 3×100×100/16×40=46.875
Correct Option: C
Answer: C
Question: If a > 0 and b < 0, which of the following are true?
I. a/b < 0
II. b/a < 0
III. a + b < 0
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: I. True, a is positive and b is negative so a/b must be negative
II. True, a is positive and b is negative so b/a must be negative
III. Not true, example: a = 5, b = -3, so a + b = 2
D
Answer: D
Question: A, B and C enter into a partnership. They invest Rs. 40,000, 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)2 : 3 : 4
B)3 : 2 : 4
C)3: 2 : 1
D)3: 4 : 7
E)none
Rationale: Sol.
A : B : C = (40000 * 36) : (80000 * 12 + 40000 * 24)
: (120000 * 24 + 40000 * 12) =144 : 192 : 336 = 3: 4 : 7
Answer D
Answer: D
Question: In the seventh grade at Parkway elementary school there are 450 students. 310 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
Options:
A)69.
B)73.
C)81.
D)91.
E)105.
Rationale: Total students = 450
Boys = 310, Girls = 140
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 140- 35 = 105.
Correct option: E
Answer: E
Question: The area of sector of a circle whose radius is 12 metre and whose angle at the center is 42° is?
Options:
A)52.7 m2
B)57.8 m2
C)52.8 metre sq
D)72.8 m2
E)52.8 m2
Rationale: 42/360 * 22/7 * 12 * 12
= 52.8 m2
Answer: C
Answer: C
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 5: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
Options:
A)4: 45 p.m.
B)5: 00 p.m.
C)5: 20 p.m.
D)5: 35 p.m.
E)7: 20 p.m.
Rationale: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 5:20 +2=7:20
Hence answer is E.Hope i am correct
Answer: E
Question: The average of 1st 3 of 4 numbers is 6 and of the last 3 are 5. If the sum of the first and the last number is 11. What is the last numbers?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: A + B + C = 18
B + C + D = 15
A + D = 11
A – D = 3
A + D = 11
2D = 8
D = 4
ANSWER:A
Answer: A
Question: In a box of 12 pens, a total of 4 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
Options:
A)1/6
B)2/33
C)14/33
D)9/16
E)3/44
Rationale: Method- 1
There are 9 fine pieces of pen and 4 defective in a lot of 12 pens
i.e. Probability of first pen NOT being defective = (8/12)
i.e. Probability of Second pen NOT being defective = (7/11) [11 pen remaining with 8 defective remaining considering that first was defective]
Probability of Both pen being NON-defective = (8/12)*(7/11) = 14/33
Answer: option C
Answer: C
Question: Insert the missing number
1, 8, 27, 64, 125, 216, (....)
Options:
A)554
B)343
C)354
D)392
E)245
Rationale: Series is 1^3,2^3,3^3,4^3,5^3,6^3,7^3
7^3=343
ANSWER:B
Answer: B
Question: If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the
stream is
Options:
A)5 km/hr
B)4 km/hr
C)2 km/hr
D)1 km/hr
E)None of these
Rationale: Explanation:
Rate upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7 - 5)kmph = 1 kmph
Answer: D
Answer: D
Question: Which of following is a leap year ?
Options:
A)2000
B)2800
C)1800
D)2600
E)3000
Rationale: The century year which is completely divisible by 400, is a leap year. Thus, the year 2800 is a leap year.
Answer : B
Answer: B
Question: if Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Options:
A)11x/y
B)11y/x
C)x/11y
D)12x/y
E)xy/11
Rationale: Answer is D
The rate of running hards: 12 minutes per y hards.
Thus the time for running x hards = x hards * 12 minutes/y hards = 12x/y
Answer: D
Question: If QR = 3(Q+ 1) + R and Q and R are integers,Q could be any of the following values EXCEPT:
Options:
A)2
B)3
C)12
D)4
E)7
Rationale: QR = 3(Q + 1) + R
QR - R = 3(Q + 1)
R = 3(Q + 1)/(Q-1)
R won't be an integer only if Q = 12 (from the options).
Answer: C
Answer: C
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
Options:
A)35 years
B)17 years
C)77 years
D)88 years
E)16 years
Rationale: Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 7)/(6x + 7) = 6/7
7(5x + 7) = 6(6x + 7) => x = 7
X's present age = 5x = 35 years.
Answer:A
Answer: A
Question: If 10 and 15 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 5
II. 15
III. 20
Options:
A)I only
B)II only
C)I and II only
D)II and III only
E)I, II, and III
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Let x be the length of the third side.
15-10 < x < 15+10
5 < x < 25
The answer is D.
Answer: D
Question: The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two will buy a pack of candy?
Options:
A)343
B)147
C)189
D)063
E)027
Rationale: •P(Buy) = 3/10, P(No Buy) = 7/10
•2 Yes, 1 No = 3/10*3/10*7/10 = 63/1000
•3 Possibilities = YYN + YNY + NYY = 3(63/1000) = 189/1000 = .189%
Answer is C.
Answer: C