divelab/Sys2Bench huggingface dataset:
Question: If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true?
I. ab is even
II. ab > 0
III. c is even
Options:
A)l only
B)ll only
C)l and ll
D)l and lll
E)l,ll,and lll
Rationale: Given: a, b, and c are integers and ab^2/c is a positive even integer.
Evaluate each option:
I. ab is even.
ab^2/c to be positive even integer ab^2 must be even, from which it follows that either a or b must be even, thus ab has to be even.
II. ab > 0
Since b is squared in our expression, then we can say nothing about its sign, thus we cannot say whether ab is positive.
III. c is even
The easiest one: ab^2/c = integer/c = even --> c could be even as well as odd.
Answer: A.
Answer: A
Question: ((-1.9)(0.6) – (2.6)(1.2))/4.0 = ?
Options:
A)1.07
B)1.0
C)-1.065
D)1.71
E)2.71
Rationale: Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.
-1.065
Answer C
Answer: C
Question: The speed of a boat in still water is 21 km/hr and the rate of current is 8 km/hr. The distance travelled downstream in 13 minutes is
Options:
A)1.6 km
B)2 km
C)6.3 km
D)4 km
E)None of these
Rationale: Explanation:
Speed downstreams	=(21 + 8)kmph
= 18 kmph.
Distance travelled	= (29 x 13/60)km
= 6.3km
Option C
Answer: C
Question: How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 4%?
Options:
A)0—1.5 gal
B)1.5—3 gal
C)3—4.5 gal
D)4.5—6 gal
E)15+ gal
Rationale: Let amount of water that must be added in gallons to dilute concentration of brine solution = x
Amount of brine already present = 10/100 * 10 = 1 gallon
1/(10+x) *100 = 4
=>100 = 40 + 4x
=> x= 60/4 = 15
Answer E
Answer: E
Question: The least number of five digits which is completely divisible by 39, is
Options:
A)10062
B)10101
C)10016
D)10023
E)11011
Rationale: D 10023
Answer: D
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 5 times, and no one scored below 600 or over 760. If the individual ranges of the three people's scores in those 5 practice tests were 20, 60 and 90, what is the difference between the maximum and minimum possible ranges of all their scores put together.
Options:
A)40
B)60
C)70
D)100
E)110
Rationale: According to the information in the question the maximum range would be between 600 and 760(160). 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 160-90 or 70.
Answer: C
Answer: C
Question: Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by
Options:
A)32.25%
B)31.00%
C)30.25%
D)30.00%
E)22.50%
Rationale: You can do this by approximation, or with straight math by calculating 100*1.15^2.
Or step by step: if you increase 100 by 15% you'll get 115, then if you increase 115=100+15 by 15% again, 100 will gain 15 again and 15 will gain its 15% which is 2.25, so total gain is 15+2.25=17.25 --> 115+17.25=132.25.
Answer: A.
Answer: A
Question: Two cyclists are running on a circular track of 600m.They start from the same point A at the same time.If they meet for the first time at a point 150 m from A, which of the following could be the possible ratio of their speeds?
Options:
A)1:3
B)2:3
C)3:5
D)5:7
E)7:11
Rationale: well, the key aspect of this question is the distance mentioned, when they met for the first time, which is 150m away from the starting point. This distance between their first meeting can be less than 600 in only two circumstance.
1) if both are travelling in the same direction and one of them has been given a head start say by few meters.
2) or if both are travelling in the opposite direction.
now since they start their journey at the same time. hence option 1 is ruled out. hence they must be running in the opposite direction. hence answer should be 1:3.
Why?? here is a solution
As here time is constant, therefore, distance traveled will be directly proportional to the the respective velocities/speed of the two runners.(d1/d2=v1/v2)
now one of them has covered 150m, therefore other must have covered 450m, therefore ratio of their speeds/velocities will be 1:3
A
Answer: A
Question: A bag holds 2 red marbles and 3 green marbles. If you removed two randomly selected marbles from the bag, without replacement, what is the probability that both would be red?
Options:
A)1/10
B)1/5
C)3/10
D)2/5
E)1/2
Rationale: probability of selecting first red marble = 2/5
probability of selecting second red marble without replacement = 1/4
final probability = 2/5 * 1/4 = 1/10
correct answer - A
Answer: A
Question: A train travels from Albany to Syracuse, a distance of 100 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours . What was the average rate of speed of the train on the return trip to Albany?
Options:
A)40
B)50
C)60
D)33.33
E)45
Rationale: 50*T =100 THEREFORE T = 100/50 =2
ON RETURN SPEED * ( 5 -2) =100 THEREFORE T = 100/3 =33.33
D
Answer: D
Question: What will be the difference in simple and compound interest on 3000 after three years at the rate of 10 percent per annum?
Options:
A)93
B)42
C)62
D)20
E)None of these
Rationale: For 3 years:
Diff.=Sum×(rate)2(300+rate)/(100)3
= 3000×10×10×310/100×100×100 = 93
Answer A
Answer: A
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
A)4
B)3
C)5
D)7
E)9
Rationale: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins
Answer: B
Answer: B
Question: 23, 29, 31, 37, 41, 43, (...)
Options:
A)53
B)48
C)59
D)47
E)50
Rationale: All are prime numbers in their order, starting from 23
Hence, next number is 47
Answer is D
Answer: D
Question: If a sample of data has mean of 23 and SD of 3, which of the following values is more than 2.5 SDs from the mean?
Options:
A)a. 16
B)b. 13.5
C)c. 17
D)d. 23.5
E)e. 26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5SD=7.5. So the value either <23-7.5=15.5 or >23+7.5=30.5.
Answer: B.
Answer: B
Question: On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder?
Options:
A)10
B)12
C)5
D)25
E)85
Rationale: Explanation:
Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
Required remainder = 5.
C)
Answer: C
Question: A wheel that has 4 cogs is meshed with a larger wheel of 12 cogs. If the smaller wheel has made 20 revolutions, what will be the number of revolutions made by the larger wheel?
Options:
A)8
B)4
C)5
D)6
E)7
Rationale: Let the number of revolutions made by the larger wheel be p
More cogs, less revolutions (Indirect proportion)
Hence we can write as
4 : 12 :: p : 20
⇒p=80/12
=7
ANSWER:E
Answer: E
Question: If the radius of a circle is increased by 20% then the area is increased by:
Options:
A)44%
B)120%
C)144%
D)40%
E)None of the above
Rationale: initially A=pi*r2
now R2=120/100r
then area=Pi*(120R/100)2
area=144R/100
that is area increases from 100 to 144=increase in area=44%
ANSWER:A
Answer: A
Question: In how many ways can the letters of word DIRECTION be arranged such that NO two vowels appear together?
Options:
A)9!
B)5!*5!
C)4!*5!/2
D)5!*4!*2!
E)6!*4!
Rationale: No 2 vowels together = the only arrangement possible will be C V C V C V C V C (with V=vowel, C=consonant). This is true as we have 4 vowels and 5 consonants and any other combination will force us to pair 2 vowels together. Since there are two 'i's divide by 2
Thus, the number of arrangements possible : 5 *4 *4 *3 *3 *2 *2*1 = 4!*5!/2 ----> C is the correct answer.
Answer: C
Question: In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 21,947. Approximately what was the percent increase?
Options:
A) 45%
B) 125%
C) 147%
D) 150%
E) 225%
Rationale: The percent increase is (21947-8902)/8902=13045/8902=1.47
So the approximate answer is C
Answer: C
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
Options:
A)20
B)40
C)80
D)140
E)60
Rationale: Explanation:
The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
Answer:E
Answer: E
Question: The average age of one class strength 32 students is 16 yrs. if the staff's age is also included, the average increases by one year. Find the age of the staff
Options:
A)50
B)52
C)49
D)32
E)35
Rationale: total age of students => 32 × 16 = 512 Yrs
Total age inclusive staff = 33 × (16+1) = 561
=> staff's age 561-512 = 49 Yrs
ANSWER C
Answer: C
Question: Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 16 more photos than Claire. How many photos has Claire taken?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: L = R
L = 3C
R = C + 16
3C = C + 16
C = 8
The answer is B.
Answer: B
Question: Candy bars are on sale at the grocery, buy 3 get 1 free. There are only 15 candy bars left (5 dark chocolate and 10 white chocolate). A shopper randomly grabs 10 bars. What is the probability the shopper will grab exactly 3 white chocolate bars?
Options:
A)7/9
B)3/5
C)40/91
D)3/7
E)7/120
Rationale: Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 4 bars from 15 bars = 15C4 = 15!/[4!(15 - 4)!] = 1,365.
To have 3 white there must be 1 dark, select 1 dark from 5 = 5C1 = 5.
And, select 3 white from 10 = 10C3 = 120.
3 white and 1 dark = (5)(120) = 600
Probability = (number outcomes favorable)/(total number outcomes) = 600/1,365 = 40/91
Answer: C
Answer: C
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 96 mph. On the way home, I flew 88 mph. What was my average speed for the trip?
Options:
A)198 mph
B)110 mph
C)92 mph
D)100 mph
E)99 mph
Rationale: (96 mph +88 mph)/2= 92 mph
Correct answer is: C
Answer: C
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 70,000, B receives :
Options:
A)14700
B)14703
C)23800
D)33777
E)34778
Rationale: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
B's share = Rs. (70000 * 17/50 ) = Rs. 23,800.
Answer: C)
Answer: C
Question: Andrea wants to fill in two sections of her
backyard with sod that must be purchased
in 2-x-2-foot squares. If the two sections
measure 30 x 40 feet and 60 x 80 feet, how
many squares of sod does she need to buy?
Options:
A)1,000
B)1,250
C)1,500
D)1,600
E)2,000
Rationale: To begin, find the area of each of the two sections by multiplying the lengths of the sides:
30 feet × 40 feet = 1,200 square feet
60 feet × 80 feet = 4,800 square feet
The total area that needs sod has an area of 1,200 + 4,800 = 6,000 square feet. Each individual
square is 2 feet by 2 feet, so each has an area of 4 square feet. Because all the numbers are
even, there will be no waste when the squares of sod are placed. Therefore, you just have
to find the number of squares needed by dividing:
6,000 ÷ 4 = 1,500
correct answer C) 1,500
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.10 per sq m?
Options:
A)6350
B)7357
C)6328
D)6750
E)7560
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 10 = Rs.6750
Answer:D
Answer: D
Question: P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 336 is divided among them . What is P's share?
Options:
A)112
B)120
C)134
D)144
E)None of these
Rationale: Explanation :
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12
= (12+30) : 4*12 : 3*12
=(4+10) : 4*4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
P's share = 378 * (7/21) = 112. Answer : Option A
Answer: A
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1: 96
B)1: 99
C)1: 94
D)1: 92
E)1: 91
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: A
Answer: A
Question: A father in his will left all his money to his children in the following manner:
$1000 to the first born and 1/10 of what then remains, then
$2000 to the second born and 1/10 of what then remains, then
$3000 to the third born and 1/10 of what then remains, and so on.
When this was done each child had the same amount. How many children were there?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: Let x be the original amount.
Let y be the amount each child gets.
The first child got y = 1000+(x-1000)/10.
The second child got y = 2000+(x-2000-y)/10.
Here, we have two equations with two unknowns. This is enough to solve for x and y.
Using the substitution method,
1000+(x-1000)/10 = 2000+(x-2000-(1000+(x-1000)/10))/10
1000+x/10-100 = 2000+x/10-200-(100+(x/10-100)/10)
1000+x/10-100 = 2000+x/10-200-100-x/100+10
x/100 = 1000-200+10
x/100 = 810
x = 81,000
The amount each child gets can be calculated this way:
y = 1000 + (x-1000)/10 = 1000 + (81000 - 1000)/10 = 9000
The number of children is the original amount of money divided by the amount of money each child gets. That's 81,000 divided by 9,000, which is 9. So there are nine children.
Answer A
Answer: A
Question: Calculate how many days it will take for 5 boys to paint a 30 m long fence if 2 boys can paint a 20 m long fence in 3 days,
Options:
A)6.80 days
B)4.80 days
C)3.80 days
D)2 days
E)1.80 days
Rationale: The length of wall painted by one boy in one day = 20 / 2 * 1/3 = 3.33 m
No. of days required to paint 50 m cloth by 8 boys = 30/ 5 *1/ 3.33 = 1.80 days.
E
Answer: E
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
Options:
A)213
B)249
C)364
D)389
E)400
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: C
Question: The Ghaziabad-Hapur-Meerut EMU and the Meerut-Hapur-Ghaziabad EMU start at the same time from Ghaziabad and Meerut and proceed towards each other at 16 km/hr and 21 km/hr respectively. When they meet, it is found that one train has travelled 60 km more than the other. The distance between two stations is:
Options:
A)445 km
B)444 km
C)400 km
D)524 km
E)None of these
Rationale: Explanation :
The two trains start simultaneously. Let they meet after a time ‘t’.
The train that has covered 60 km more must be the faster of the two.
Hence,
=>60=(21–16)×t.
=>t=12 hours.
Since they are traveling towards each other, total distance is the sum of the distances travelled by the two trains individually.
Total distance = 16×12+21×12 = 444 Km.
Answer : B
Answer: B
Question: If 80 lamps can be lighted 5 hours per day for 10 days for Rs. 21.25,then the number of lamps which can be lighted 4 hours daily for 30days for Rs. 76.50, is?
Options:
A)100
B)110
C)120
D)130
E)None of these
Rationale: Explanation :
(Hrs/Day 4: 5) : (Money 21.25 :76.50) : (Days 30:10) : : 80 : x4 * 21.25 * 30 * x = 5 * 76.50 * 10 * 80 so x = 120
Answer : C
Answer: C
Question: What should be added to 4329 so that it may become a perfect square?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: 66x66=4356
4356-4329 = 27
If added to 27 get perfect square
answer =D
Answer: D
Question: If anangletis defined as 1 percent of 1 degree, then how many anglets are there in one half circle?
Options:
A)0.36
B)3.6
C)360
D)18,000
E)36,000
Rationale: 1 degree * 1/100 = 1 anglet
So 1 degree = 100 anglets
=> 180 degrees = 18,000 anglets
Answer - D
Answer: D
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is?
Options:
A)186
B)278
C)119
D)278
E)272
Rationale: Number of words which can be formed
= 5! - 1 = 120 - 1
= 119.
Answer:C
Answer: C
Question: If 6 spiders make 6 webs in 6 days, then 1 spider will make 1 web in how many days?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:6
Webs 6:1
1 x 6 x x = 6 x 1 x 6
=> x= 6
Answer is B
Answer: B
Question: An astronomer noted that a grouping of red giant stars had an average solar mass of 8 M each, and a grouping of white dwarf stars had an average solar mass of 1.5 M each. If the astronomer calculated the total solar mass of both groupings to be 49 M, what total number of red giant stars and white dwarf stars did the astronomer note?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: We can determine quickly that total number should range between 49/8 <= N <=49/1.5 , so ans should be between 6 and 33.
Now solving the expression 8A+1.5B =49
decreasing 49 in multiple of 8 and checking divisibility of that number by 1.5. this way we get
2 red giants, 22 white dwarfs we get 49, but 2 + 22 = 24 and 24 is not an option.
Next we get 5 red giants and 6 white dwarfs to get 49, 5*8 + 6*1.5 = 49
Hence total number is 5 + 6 = 11
Ans B
Answer: B
Question: A train is travelling at 48 kmph. It crosses another train having half of its length, travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in
45 seconds. What is the length of the platform?
Options:
A)400 m
B)500 m
C)600 m
D)550 m
E)700 m
Rationale: speed of I train = 48kmph
length of I train = 2x m
speed of sec train = 42 kmph
length of seconf train = x m
dist = (2x+x) = 3x m
time = 12 sec
= 90 * 5/18 = 25m/s
x=100
length of first train = 2x = 200 m
time taken = 45 sec
speed of first train = 48 kmph = 48 * 5/18 = 40/3 m/s
length of the platform = y metre
200 + y = 45 * 45/3 = 600
y = 400
ANSWER A
Answer: A
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
Options:
A)1/48
B)1/42
C)1/40
D)1/41
E)1/43
Rationale: 2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer: B
Answer: B
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)45
B)60
C)75
D)90
E)120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer: Option D
Answer: D
Question: In an election, candidate A got 60% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate.
Options:
A)285600
B)340000
C)347000
D)356000
E)357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 60 %
Therefore, the number of valid votes polled in favour of candidate A = 60 % of 476000
= 60/100 × 476000
= 28560000/100
= 285600
A)
Answer: A
Question: A can run 288 metre in 28 seconds and B in 32 seconds. By what distance A beat B?
Options:
A)38 metre
B)28 metre
C)23 metre
D)15 metre
E)36 metre
Rationale: Clearly, A beats B by 4 seconds
Now find out how much B will run in these 4 seconds
Speed of B = Distance/Time taken by B=288/32=9 m/s
Distance covered by B in 4 seconds = Speed Ã— time =9Ã—4=36 metre
i.e., A beat B by 36 metre
Answer is E
Answer: E
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 12 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
Options:
A)12/7
B)4/1
C)2/3
D)3/4
E)3/2
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+12) = 36/21 = 12/7.
Answer: A.
Answer: A
Question: The banker’s discount on Rs.1600 at 15% per annum is the same as true discount on Rs.1680 for the same time and at the same rate. The time is
Options:
A)3 months
B)4 months
C)6 months
D)8 months
E)10 months
Rationale: Solution
S.I on Rs. 1600 = T.D on Rs. 1680.
Rs.1600 is the P.W of Rs.1680.
Rs.80 is S.I on Rs.1600 at 15%.
Time	= (100x80 / 600x15)
= 1/3 year
= 4 months.
Answer B
Answer: B
Question: The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 16 and 17. The larger of the two numbers is:
Options:
A)338
B)278
C)322
D)231
E)391
Rationale: Clearly, the numbers are (23 * 16) and (23 * 17). Larger number
= (23 * 17) = 391.
Answer: E
Answer: E
Question: Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 24% ryegrass and 75% fescue. If a mixture of X and Y contains 36% ryegrass, what percent of the weight of the mixture is from mixture X?
Options:
A)25%
B)40%
C)60%
D)75%
E)90%
Rationale: 36% is 12%-points above 25% and 4%-points below 40%.
Thus the ratio of mixture Y to mixture X is 1:3.
The percent of mixture X is 3/4 = 75%.
The answer is D.
Answer: D
Question: The sale price sarees listed for Rs.350 after successive discount is 20% and 5% is?
Options:
A)266
B)278
C)342
D)787
E)191
Rationale: 350*(80/100)*(95/100)
= 266
Answer: A
Answer: A
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
9 minutes more to walk to work than to ride his bicycle, then x equals
Options:
A)4
B)7
C)10
D)15
E)13.5
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 9 mins or 9*60 secs in 9*60/40 =13.5 km
ANSWER:E
Answer: E
Question: The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 45, then how long is the base of isosceles triangle?
Options:
A)5 units
B)10 units
C)15 units
D)20 units
E)25 units
Rationale: The base of the isosceles triangle is 45-20-20= 5 units
The answer is A.
Answer: A
Question: Arnold and Danny are two twin brothers that are celebrating their birthday. The product of their ages today is smaller by 5 from the product of their ages a year from today. What is their age today?
Options:
A)2.
B)4.
C)5.
D)7.
E)9.
Rationale: ad = (a+1) (d+1) -5
0= a+d-4
a+d = 4
a=d (as they are twin brothers)
a=d=2
A is the answer
Answer: A
Question: The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After
6 years, what will be son's age?
Options:
A)23 years
B)22 years
C)21 years
D)20 years
E)18 years
Rationale: Let the present age of the son = x
Then present age of the father = (60 - x)
six years ago father's age was 5 times the age of the son
(60-x)-6 = 5(x-6)
x = 84/6 = 14
son's age after 6 years
x+6 = 14 + 6 = 20
ANSWER D
Answer: D
Question: The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.18000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is
Options:
A)20
B)21
C)42
D)23
E)24
Rationale: Solution
Let the toatl number of workers be x.
Then 8000x=(18000 x 7) + 6000 (x -7)
x= 42
Answer C
Answer: C
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)3/17
C)4/26
D)3/19
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