divelab/Sys2Bench huggingface dataset:
Question: A box contains SEVEN bulbs out of which 4 are defective. If THREE bulbs are chosen at random, find the probability that atleast one bulb is good
Options:
A)5/38
B)4/39
C)4/31
D)4/35
E)6/35
Rationale: Required probability = 1-4C3/7C3=1 - 4/35 = 31/35.Answer:D
Answer: D
Question: The ages of 2 persons differ by 38 years. If 12 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.
Options:
A)30.5
B)48.5
C)50.4
D)62.6
E)57.6
Rationale: age of the younger person = x
age of the elder person = x+38
6(x-12) = x+38-12
x= 19.6
age of elder person = 19.6+38=57.6
Answer is E
Answer: E
Question: A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
Options:
A)8 km/hr, 1 km/hr
B)5 km/hr, 4 km/hr
C)1 km/hr, 6 km/hr
D)2 km/hr, 1 km/hr
E)4 km/hr, 1 km/hr
Rationale: Downstream speed=72km/8hrs
=9kmph
upstream speed=84km/12hrs
=7kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(9+7)/2kmph
=8kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(9-7)/2kmph
=1kmph
ans is 8km/hr,1km/hr
ANSWER:A
Answer: A
Question: If a^2 = b^2, which of the following must be true?
Options:
A)|a| = |b|
B)a = −b
C)a = |b|
D)a = −|b|
E)a = b
Rationale: Since a^2=b^2 we have 0=a^2 – b^2 =(a-b)*(a+b). So a=b or a=-b.
So only (E) and only (B) cannot be an answer.
The choice (C) tells us that k should be greater than or equal to 0.
Similarly the choice (D) tells us that k should be less than or equal to 0.
So neither (C) nor (D) cannot be the answer.
The answer is, therefore, (A).
Answer: A
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A
Options:
A)Rs.300
B)Rs.56
C)Rs.100
D)Rs. 240
E)Rs.90
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 =Rs. 240
ANSWER:D
Answer: D
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 880 in 4 years. The
rate on interest per annum is.
Options:
A)4%
B)5%
C)6%
D)7%
E)10%
Rationale: Explanation:
S.I. on Rs 800 for 1 year = 80
Rate = (100*80)/(800*1) = 10%
Answer: E
Answer: E
Question: A worker is paid a regular rate of $0.10 for completing a survey. The worker completes 50 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 30% higher than her regular rate. If she completed 35 surveys involving the use of her cellphone, how much did she get that week?
Options:
A)$13
B)$9
C)$10.50
D)$1.50
E)$12
Rationale: $10(0.3)=$0.30 per each survey involving the use of her cell phone
$30(35)=$10.50 for completing surveys involving the cell phone
$0.10(50-35)=$0.10(15)=$1.50
Total $1.50+$10.50=$12
Answer E 12.
Answer: E
Question: 90 + 5 * 12 / (180/3) = ?
Options:
A)23
B)78
C)27
D)91
E)81
Rationale: Explanation:
90 + 5 * 12 / (180/3) = 90 + 5 * 12 / (60)
= 90 + (5 * 12)/60 = 90 + 1 = 91.
Answer:D
Answer: D
Question: For any non-zero a and b that satisfy |ab| = ab and |b| = -b
|b - 4| + |ab - b| = ?
Options:
A)a) ab - 4
B)b) 2b - ab - 4
C)c) ab + 4
D)d) ab - 2b
E)e) ab - 2b + 4
Rationale: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4
Answer: Option E
Answer: E
Question: One-sixth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
Options:
A)4%
B)5%
C)6%
D)11%
E)16%
Rationale: 1/6 of the switches are defective.
The defective switches that are not rejected are 1/5*1/6 = 1/30 = 4/120 of all switches.
The non defective switches that are sold are 5/6*19/20 = 95/120 of all switches.
The percent of switches sold that are defective is 4/99 which is about 4%.
The answer is A.
Answer: A
Question: Which one the following fractions has the exact division of nine?
Options:
A)47776/9
B)37777/9
C)87777/9
D)57777/9
E)67777/9
Rationale: Numerator for all option is 9. If the numerator value digits are added together and forms the number equal to 9, then it is exact division of 9. So Option (C) 8+7+7+7+7 = 36= 3+6 = 9. Answer (C).
Answer: C
Question: The 5 th term and 21 st term of a series in A.P are 10 and 42 respectively. Find the 31 st term.
Options:
A)50
B)55
C)65
D)62
E)52
Rationale: a + 4d = 10 ………….. (1)
a + 20d = 42 ………….. (2)
Eqn (2) – Eqn (1) gives 16d = 32 , d = 2
Substituting d =2 in either (1) or (2), a = 2.
31 st term = a + 30d = 2 + 30*2 = 62
ANSWER: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 this son is
Options:
A)21 years
B)22 years
C)23 years
D)24 years
E)25 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+24.
=> 2(x+2) = (x+24+2)
=> 2x+4 = x+26
=> x = 22 years
Answer: Option B
Answer: B
Question: (xn - an) is completely divisible by (x - a), when
Options:
A)n is any natural number
B)n is an even natural number
C)n is and odd natural number
D)n is prime
E)None
Rationale: For every natural number n, (xn - an) is completely divisible by (x - a).
A)
Answer: A
Question: How many kg of pure salt must be added to 100kg of 10% solution of salt and water to increase it to a 15% solution?
Options:
A)A)5.8
B)B)1.3
C)C)9.6
D)D)12.5
E)E)7.9
Rationale: Amount salt in 100kg solution = 10*100/100 = 10 kg
Let x kg of pure salt be added
then(10+x)/(100+x)=15/100
200+20x=300+3x
17x = 100
x = 5.8
Answer is A
Answer: A
Question: Carol is four times Alice’s age but only twice as old as Betty. Alice is thirty-six years younger than Carol. How old is Betty?
Options:
A)36
B)39
C)42
D)48
E)24
Rationale: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.
We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 4 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 36 years older than Alice
We're asked for BETTY'S age.
Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST smaller answer first.
IF....
Betty = 24
Then Carol = 2(24) = 48
Then Alice = 48 - 36 = 12 AND 48/4 =12
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 24
E
Answer: E
Question: x+(1/x) = 1.5 find x^2 + (1/x^2)
Options:
A)2.25
B)3.25
C)4.25
D)5.25
E)0.25
Rationale: squaring on both sides (x+1/x)^2=1.5^2
x^2+1/X^2=2.25-2
x^2+1/X^2=0.25
ANSWER:E
Answer: E
Question: If a coin is tossed 6 times what is the probability that it will land either heads 6 times or tails 6 times?
Options:
A)1/4
B)1/8
C)1/16
D)1/32
E)1/64
Rationale: The probability of 6 heads is (1/2)^6 = 1/64
The probability of 6 tails is (1/2)^6 = 1/64
The probability of 6 heads or 6 tails is 1/64 + 1/64 = 1/32
The answer is D.
Answer: D
Question: The ages of two persons differ by 16 years. 7 years ago, the elder one was 3 times as old as the younger
one. What are their present ages of the elder person
Options:
A)15
B)31
C)25
D)30
E)35
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x � 16
(x � 7) = 3 (x-16-7)
=> x � 7 = 3x � 69
=> 2x = 62
=> x = 62/2 = 31
Answer: Option B
Answer: B
Question: The perimeter of a square is equal to the radius of a circle having area 39424 sq cm, what is the area of square?
Options:
A)1225 sq cm
B)441 sq cm
C)784 sq cm
D)Can’t say
E)None of these
Rationale: Let the side of square =a cm and radius of circle=r cm
Given, 4a= r
Also Area of square= Pi*r^2= 39424, r^2=12544 or r=112
So a= r/4= 112/4=28
Hence Area of square=a^2=28^2=784 cm^2
ANSWER:C
Answer: C
Question: The sum of 11 hours 45 minutes and 2 hours 15 minutes is approximately what percent of a day?
Options:
A) approx 54%
B) approx 58%
C) approx 74%
D) 28%
E) 72%
Rationale: Since the question is asking for an approximate percentage
11:45+2:15 ~ 14 hours
% of day = 14*100/24 ~ 58%
Answer is B.
Answer: B
Question: How much time will take for an amount of Rs. 450 to yield Rs. 78 as interest at 4.5% per annum of simple interest?
Options:
A)8 years
B)3 years 10 months
C)3 years
D)9 years
E)5 years
Rationale: Time = (100 * 78) / (450 * 4.5)
= 3 years 10 months
Answer: B
Answer: B
Question: The average weight of 36 men is 50 kg. It was found later that the figure of 37 kg was misread as 73 kg. What is the correct average?
Options:
A)49 kg
B)51 kg
C)50.5 kg
D)51.5 kg
E)None of these
Rationale: Correct average = [( 50 x 36) - 73 + 37 )]/36 = 1764/36 = 49 kg.
ANSWER:A
Answer: A
Question: A snooker tournament charges $45.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 300 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
Options:
A)212
B)240
C)220
D)230
E)225
Rationale: let no of sits in vip enclosure is x then x*45 +15( 300-x) =7500 or 30x = 7500 -4500 , x = 3000/30 =100
vip =100 general 220
C
Answer: C
Question: Adam borrowed some money at the rate of 6% p.a. for the first two years , at the rate of 9% p.a. for the next three years , and at the rate of 14% p.a. for the period beyond five years. 1£ he pays a total interest of Rs. 11,400 at the end of nine years how much money did he borrow?
Options:
A)Rs.8,000
B)Rs.09,000
C)Rs.11,000
D)Rs.10,000
E)Rs.12,000
Rationale: Let the sum borrowed be x. Then,
(x*2*6)/100 + (x*9*3)/100 + (x*14*4)/100 = 11400
(3x/25 + 27x/100 + 14x / 25) = 11400
95x/100 = 11400
x = (11400*100)/95 = 12000.
Hence , sum borrowed = Rs.12,000
Answer is E.
Answer: E
Question: The average of first 10 odd numbers is?
Options:
A)11
B)10
C)87
D)26
E)39
Rationale: Sum of 10 odd no.
= 100
Average = 100/10
= 10
Answer:B
Answer: B
Question: In a village of 100 households, 80 have at least one DVD player, 90 have at least one cell phone, and 65 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, x – y is:
Options:
A)65
B)55
C)45
D)30
E)20
Rationale: Am I missing something here??? it seems straightforward......
The obvious maximum that have all 3 is 65, because you are limited by the SMALLEST number.
The minimum is simply the sum of the max of each people who DONT have the product, so:
100-90 = 10 don't have Cell
100-80 = 20 don't have DVD
and 100-65 = 35 don't have MP3
SO a total of 10+20+35 = 65 combined who might NOT have SOME combination of the 3 products. So subtract that from 100, to give you the minimum of the people who COULD have all 3 and you get 100-65 = 35.
65-35 = 30
D
Answer: D
Question: 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds
Options:
A)11:9
B)13:9
C)17:9
D)21:9
E)None of these
Rationale: Explanation:
We know total distance is 200 Km
If both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [110+90=200km]
So ratio of their speed = 110:90 = 11:9
Option A
Answer: A
Question: If 2 persons can do 2 times of a particular work in 2 days, then, 7 persons can do 7 times of that work in?
Options:
A)2 days
B)4 days
C)6 days
D)7 days
E)8 days
Rationale: That is, 1 person can do one time of the work in 2 days.
Therefore, 7 persons can do 7 times work in the same 2 days itself
A)
Answer: A
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical A required to keep the reaction rate unchanged.
Options:
A)100 % decrease
B)50% decrease
C)40% decrease
D)40% increase
E)50% increase
Rationale: r = k A^2 / B for some constant k<>0
(Question should also give B<>0)
So we have
r1 = k A1^2 / B1
r2 = k A2^2 / B2
r1 = r2
B2 = (1+100%)B1 = 2B1
k A1^2 / B1 = k A2^2 / B2
A1^2 / B1 = A2^2 / 2B1
2A1^2 = A2^2
(sqrt(2)A1)^2 = A2^2
A1,A2>0
A2 = sqrt(2) * A1
A2 = (1 + 41.4%) * A1
About 40% increase
ANSWER:C
Answer: C
Question: in how many can the letters of the word COLLEGE be arranged,such that its vowels do not come together?
Options:
A)980
B)920
C)1020
D)1060
E)1080
Rationale: COLLEGE
C=1,O=1,G=1, L=2,E=2
vowels = O E E
total no. of words formed = 7!/(2!*2!) = 7!/4 = 1260
no. of words when vowels come together = CLLG(OEE) => 5!/2! * 3!/2! = 180
no. of words having vowels not together = 1260 - 180 = 1080
ANSWER:E
Answer: E
Question: One-fourth of the boys and three-eighth of the girls in a school participated in the sports. What fractional part of the total student population of the school participated in the annual sports ?
Options:
A)4/12
B)5/8
C)8/12
D)Data inadequate
E)None of these
Rationale: Explanation:
Boys and girls ratio was not given.
Correct Option:D
Answer: D
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
Options:
A)150
B)330
C)277
D)279
E)712
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer:A
Answer: A
Question: A room 13 m 47 cm long and 7m 77 cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
Options:
A)116636
B)116406
C)116647
D)116291
E)116675
Rationale: Explanation:
Area of the room = (1347 x 777) cm2.
Size of largest square tile = H.C.F. of 1347 cm and 777 cm = 3 cm.
Area of 1 tile = (3 x 3) cm2.
Number of tiles required =(1347×777)/(3×3)=116291
Answer: Option D
Answer: D
Question: A man has Rs. 240 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)45
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 240
16x = 240
x = 15.
Hence, total number of notes = 3x = 45.
Answer: Option E
Answer: E
Question: For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”3?
Options:
A)5
B)3
C)2
D)1
E)0
Rationale: 4”3= 9 - 4=5
Answer: A
Answer: A
Question: The ratio of pens to pencils is 5 to 6. There are 8 more pencils than pens. How many pencils are there?
Options:
A)30
B)32
C)48
D)55
E)64
Rationale: Let x equal the number of pens, and y the number of pencils.
Then, x = 5/6y.
We also know that x = y - 8. And so, we can substitute:
y - 8 = 5/6y
So to isolate y, we get:
1/6y = 8
And therefore:
y = 48
Answer: C
Answer: C
Question: Find √? /15= 4 ?
Options:
A)76
B)5776
C)304
D)3600
E)None
Rationale: Answer
Let √N/15= 4
Then √N = 15 x 4 = 60
∴ N = 60 x 60 = 3600.
Correct Option: D
Answer: D
Question: We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 10, and the difference between the total number of strawberries and the total number of blueberries would increase by 50. Each blue box contains how many blueberries?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: Let x be the number of blueberries in each blue box.
Then there are x+10 strawberries in each red box.
x+(x+10)=50
x = 20
The answer is C.
Answer: C
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 7?
A. 48 kmph
Options:
A)33
B)54
C)28
D)27
E)16
Rationale: Let the distances between city A to B and B to C be 2x km and 7x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (7x)/60 = (6x + 14x)/120 = 20x/120 = x/6 Average speed = (2x + 7x)/(x/6) = 54 kmph.
Answer: B
Answer: B
Question: A man can row with a speed of 25 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)A)25
B)B)28
C)C)20
D)D)21
E)E)30
Rationale: M = 25
S = 5
DS = 25 + 5 = 30
Answer:E
Answer: E
Question: In Cliff’s impressive rock collection, there are half as many igneous rocks as sedimentary rocks. Of the igneous rocks, 3/5 are shiny and the rest are matte, while 1/5 of the sedimentary rocks are shiny. If there are 30 shiny igneous rocks, how many total rocks does Cliff have?
Options:
A)30
B)45
C)60
D)150
E)135
Rationale: We can start with the known quantity and then go on to find the others.
Shiny igneous ricks are 30. These are (3/5) of total igneous rocks.
(3/5)*Total igneous rocks = 30
Total igneous rocks = 30 * (5/3) = 50
Total sedimentary rocks = 2*Total igneous rocks = 2*50 = 100
Total number of rocks = 50 + 100 = 150
Answer (D)
Answer: D
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is?
Options:
A)8876
B)2765
C)6000
D)1298
E)1261
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18000 = 6000
Answer:C
Answer: C
Question: If air is called green , green is called blue, blue is called tangerine, sky is called yellow, yellow is called water and water is called pink, then what is the color of clear sky ?
Options:
A)Blue
B)Sky
C)Water
D)Tangerine
E)Black
Rationale: Explanation:The colour of clear sky is 'blue' and as given, 'blue' is called 'tangerine'.So, the colour of clear sky is 'tangerine'.Answer: D
Answer: D
Question: A store raised the price of an item by exactly 15 percent. Which of the following could NOT be the resulting price of the item?
Options:
A)115
B)230
C)345
D)460
E)300
Rationale: If it raised the value by 15% then the resulting price is 1.15 times the original price. So the final answer has to be a multiple of 1.15. Check the answers.
115 - Yes
230 - Yes
345 - Yes
460 - Yes
300 - No
Answer : E
Answer: E
Question: Donovan took a math test and got 35 correct and 13 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
Options:
A)57.78%
B)67.78%
C)72.92%
D)47.78%
E)97.78%
Rationale: 35 correct our of 48 total (35+13)
35/48
correct answer C
Answer: C
Question: What is the two-digit number?
I.
The difference between the two-digit number and the number formed by interchanging the digits is 27.
II.
The difference between the two digits is 3.
III.
The digit at unit's place is less than that at ten's place by 3.
Options:
A)I and II
B)II and III
C)All
D)I and either II or III
E)Even with all I, II and III, answer cannot be give.
Rationale: Let the tens and units digit be x and y respectively.
I. (10x + y) - (10y + x) x - y = 3.
II. x - y = 3.
III. x - y = 3.
Thus, even all the given three statements together do not give the answer.
Correct answer is (E).
Answer: E
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options:
A)11
B)18
C)92
D)27
E)28
Rationale: Explanation:
=> 2l + 2b = 5b
=> 3b = 2l
b=(2/3)l
Then, Area = 216 cm2
=> l x b = 216
=> l x (2/3)l =216
=> l2 = 324
l = 18 cm.
Answer: B) 18
Answer: B
Question: 14. The sum and the product of two numbers are 25 and 144 respectively, the difference of the number is?
Options:
A)7
B)9
C)8
D)5
E)4
Rationale: x + y = 25
xy = 144
(x- y)2 = (x + y)2 â€“ 4xy
(x- y)2 = 625 â€“ 576 => (x â€“ y) = 7
ANSWER: A
Answer: A
Question: How long will it take a train travelling at 98kmph to pass an electric pole if the train is 140 m long
Options:
A)6.15
B)5.15
C)3.15
D)1.15
E)7.15
Rationale: Sol.
Speed = [ 98x5/18] m/sec =27.2 m / sec.
Time taken = (140/27.2)sec =5.15 sec.
Answer B
Answer: B
Question: A third of Arun’s marks in mathematics exceeds a half of his marks in English by 80.if he got 240 marks In two subjects together how many marks did he got in English?
Options:
A)180,60
B)150,80
C)140,70
D)120,90
E)None of them
Rationale: Let Arun’s marks in mathematics and english be x and y
Then 1/3x-1/2y=30
2x-3y=180……>(1)
x+y=240…….>(2)
solving (1) and (2)
x=180
and y=60
Answer is A.
Answer: A
Question: 15 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required?
Options:
A)10days
B)11days
C)9days
D)8days
E)12days
Rationale: That is, 1 work done = 15 × 8 × 10
Then, 12 8 × 10 = ? × 15 × 8
? (i.e. No. of men required) = 15 × 8 × 10/15× 8 = 10 days
A)
Answer: A
Question: If x, y, and z are positive integers and 3x = 2y = 4z, then the least possible value of x + y + z is
Options:
A)15
B)25
C)30
D)42
E)13
Rationale: given 3x=2y=4z
x+y+z in terms of x
= x+(3x/2)+(3x/4) = 26x/8=13x/4
now checking with each of the answers and see which value gives a minimum integer value.
A x = 4/13*15 , not an integer
B,C,E can be ruled out similarly.
D is minimum value as x = 13*4/13 = 4
Answer is E
Answer: E
Question: How many integers between 4000 and 5000 that have distinct digits and increase from left to right ?
Options:
A)10
B)48
C)60
D)20
E)600
Rationale: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
445_ --> 4
446_ --> 3
447_ --> 2
448_ --> 1
456_ --> 3
457_ --> 2
458_ --> 1
467_ --> 2
468_ --> 1
478_ --> 1
Number of integers =20
D
Answer: D
Question: A certain rectangular window is two times as long as it is wide. If its perimeter is 30 feet, what are its dimensions in terms of length by width?
Options:
A)12 by 2
B)11 by 3
C)10.5 by 3.5
D)10 by 5
E)9 by 3
Rationale: 2x+2y=30
x+y=15
x+2x=15
3x=15
x=5
Answer D
Answer: D
Question: 4 gentlemen and 3 gentlewomen are candidates for 2vacancies. A voter has to vote for 2 candidates. In how many ways can one cast his vote?
Options:
A)11
B)12
C)15
D)16
E)21
Rationale: There are 7 candidates and a voter has to vote for any two of them.
So, the required number of ways is,
= 7C2 = 21.
E
Answer: E
Question: 125 students of a school are about embarking on a trip. What is the least number of vans needed to convey them given that each van will only take 10 students each?
Options:
A)12
B)11
C)13
D)18
E)10
Rationale: To find the number of vans, we divide 125 by 10.
125/10 = 12 and remainder = 5
So 10 vans are needed to transport 125 students, and 1 van is needed to transport the 5 remaining students. A total of 11 vans are needed.
correct answer B
Answer: B
Question: Convert 0.36 in to a vulgar fraction ?
Options:
A)18/50
B)16/50
C)17/50
D)9/25
E)None
Rationale: Answer
0.36 = 36/100 = 9/25
Correct Option: D
Answer: D
Question: A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 60. When the number of legs was counted, the number totaled up to 160. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.
Options:
A)16
B)20
C)24
D)28
E)32
Rationale: Let x be the number of chickens.
Then 60-x is the number of pigs.
2x+4(60-x)=160
2x=80
x=40 (chickens)
60-x=20 (pigs)
There are 40-20=20 more chickens on the farm.
The answer is B.
Answer: B
Question: If the sides of a triangle are 26 cm, 25 cm and 10 cm, what is its area?
Options:
A)120
B)110
C)130
D)140
E)125
Rationale: The triangle with sides 26 cm, 25 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 25 * 10 = 125 cm2
Answer: Option E
Answer: E