divelab/Sys2Bench huggingface dataset:
Question: A courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is :
Options:
A)16000
B)18000
C)20000
D)22000
E)None of these
Rationale: Explanation:
Number of bricks =Courtyard area /1 brick area
=(2500×1600 /20×10)=20000
Option C
Answer: C
Question: In what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)3
B)5
C)9
D)4
E)7
Rationale: T = 40/36 * 18/5 = 4 sec
Answer:D
Answer: D
Question: In the coordinate plane a slope of the line K is 0.5 times the y-intercept of the line K. What is the x-intercept of the line K?
Options:
A)-4
B)4
C)-2
D)1/2
E)-2
Rationale: As Y=0.5mx+m, from 0=1/2mx+m we get x=-2. Hence, the correct answer choice is E.
Answer: E
Question: There are between 70 and 80 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
Options:
A) 71
B) 73
C) 76
D) 77
E) 79
Rationale: Let number of cards = x
If the cards are counted 3 at a time , there are 2 left over-
x= 3p+2
x can take values 71 , 77
If the cards are counted 4 at a time , there is 1 left over
x= 4q+1
x can take values 73, 77
Therefore , x = 77
Answer D
Answer: D
Question: From below option 49 is divisible by which one?
Options:
A)A)2
B)B)3
C)C)4
D)D)5
E)E)7
Rationale: 49/7 = 7
E
Answer: E
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)3388
B)3120
C)2177
D)1987
E)1268
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: B
Question: Sum of two numbers is 30. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
Options:
A)A)5
B)B)9
C)C)11
D)D)13
E)E)15
Rationale: Explanation:
x + y = 30
2x – 3y = 5
x = 19 y = 11
C)
Answer: C
Question: On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄2 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 200 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?
Options:
A) 250
B) 300
C) 800
D) 400
E) 550
Rationale: Let D = total distance
Traci traveled 1/2 = D/2
i.e. remaining distance = D/2
She traveled 1/4 th of D/2 = D/8
Thus:
D = (D/2) + (D/8) + 200
D = 800
ANSWER: C
Answer: C
Question: (3108 + 6160) / 28
Options:
A)380
B)350
C)331
D)310
E)None of these
Rationale: Explanation:
As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9268)/28 = 331
Option C
Answer: C
Question: A pipe takes a hours to fill the tank. But because of a leakage it took 3 times of its original time. Find the time taken by the leakage to empty the tank
Options:
A)50 min
B)60 min
C)90 min
D)80 min
E)70 min
Rationale: pipe a can do a work 60 min.
lets leakage time is x;
then
1/60 -1/x=1/180
x=90 min
ANSWER:C
Answer: C
Question: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?
Options:
A)267
B)766
C)810
D)868
E)812
Rationale: 12 men 120 acres 36 days
54 men ? 54 days
120 * 54/12 * 54/36
10 * 54 * 3/2
54 * 15 = 810
Answer:C
Answer: C
Question: A and B together can complete work in 4 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B?
Options:
A)4
B)8
C)5
D)6
E)7
Rationale: Explanation:
(A+B) one day work =1/4
now A does half of the work in 3 days so A can complete the whole work in 6 days
A’s one day work =1/6
B’s one day work=1/4 - 1/6= 1/12
B alone can complete the work in 12 days so half of the work in 6 days
Answer: Option D
Answer: D
Question: A container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 9 ounces of a solution that is 1 part alcohol to 2 parts water. What is the ratio of alcohol to water in the resulting solution?
Options:
A)1:2
B)3:7
C)3: 5
D)4:7
E)7:3
Rationale: Container 1 has 12 ounces in the ratio 1:2
or,
x+2x=12 gives x(alcohol)=4 and remaining water =8
container 2 has 9 ounces in the ratio 1:2
or,
x+2x=9 gives x(alcohol)=3 and remaining water =6
mixing both we have alcohol=4+3 and water =8+6
ratio thus alcohol/water =7/14=1/2
Answer A
Answer: A
Question: In a class, 30% of the students speaks truth, 20% speaks lie and 10% speaks both. If a student is selected at random, what is the probability that he has speak truth or lie?
Options:
A)1/4
B)2/3
C)3/5
D)2/5
E)2/7
Rationale: D) 2/5
Answer: D
Question: If a certain sample of data has a mean of 21.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)13.5
C)17.0
D)23.5
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 2.5*SD=7.5. So the value must be either less than 21-7.5=13.5or more than 21+7.5=28.5.
Answer: B.
Answer: B
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
Options:
A)3 9/19 hrs
B)3 9/77 hrs
C)3 9/17 hrs
D)3 9/57 hrs
E)3 9/27 hrs
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.Answer: C
Answer: C
Question: What is the remainder when 1024*1047*1050*1053 is divided by 33?
Options:
A)3
B)27
C)30
D)21
E)18
Rationale: take the remainder from each of 1024/33, 1047/33 and so on..
1024/33 gives remainder = 1
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e =1*24*27*30
break them into pairs 1*24/33 gives remainder 24
and 27*30/33 gives remainder 18
so 24*18/33 gives remainder 3.
A
Answer: A
Question: Q and R are two-digit positive integers that have the same digits but in reverse order. If the positive difference between Q and R is less than 20, what is the greatest possible value of Q minus R?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: A two-digit integer "ab" can be expressed algebraically as 10a+b.
Q-R=(10a+b)-(10b+a)=9(a-b)<20.
The greatest multiple of 9 which is less than 20 is 18.
The answer is D.
Answer: D
Question: Ram and shyam start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
Options:
A)65
B)60
C)55
D)50
E)45
Rationale: let x=length of pool
at first meeting, combined distance=x
at second meeting, combined distance=3x
if andy swims 18.5 m of x, then he will swim 3*18.5=55.5 m of 3x
andy's total distance to second meeting=x+10.5 m
x+10.5=55.5 m
x=45 m
E
Answer: E
Question: Which of the following CANNOT be the least common multiple of two positive integers x and y
Options:
A)xy
B)x
C)y
D)xy - y
E)x + y
Rationale: The least common multiple of two positive integers cannot be less than either of them. Therefore, since xy - y is less than x, it cannot be the LCM of a x and y.
Answer: D
Answer: D
Question: The integer x is divisible by both 9 and 36. Which of the following must be an integer?
Options:
A)x/16
B)x/36
C)x/25
D)x/46
E)x/24
Rationale: Prime factorization of 9 = 3^2
Prime factorization of 36= 3^2*2^2
LCM of 9 and 36 = 3^2 * 2^2 = 36
Therefore x/36 must be an integer
Answer B
Answer: B
Question: The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:
Options:
A)0.02
B)0.2
C)0.04
D)0.4
E)none
Rationale: Given expression = (11.98)^2 + (0.02)^2 + 11.98 * x.
For the given expression to be a perfect square, we must have
11.98 * x = 2 * 11.98 * 0.02 or x = 0.04
Answer = C
Answer: C
Question: In a certain neighborhood, there are half as many beige houses as white houses, and 8 times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
Options:
A)8:3
B)1:6
C)5:1
D)2:3
E)1:4
Rationale: The ratio of beige:white:brown = 4:8:1
The answer is E.
Answer: E
Question: The perimeter of a rectangular yard is completely surrounded by a fence that measures 18 meters. What is the length of the yard if the area of the yard is 20 meters squared?
Options:
A)8
B)2
C)7
D)5
E)1
Rationale: Perimeter of rectangular yard = 2(l + b) = 18 --> l + b = 9
Area = l * b = 20
b = 9 - l
l(9 - l) = 20
29l - l^2 = 20
l^2 - 9l + 20 = 0
Upon simplifying we get l = 5 or 4. Only 5 is there in the answer choice.
Answer: D
Answer: D
Question: On a map, 1 inch represents 28 miles. How many inches would be necessary to represent a distance of 383.6 miles?
Options:
A)5.2
B)7.4
C)13.7
D)21.2
E)28.7
Rationale: 28 miles represented by 1 inch
1 mile represented by (1/28) inch
383.6 miles represented by (1/28) * 383.6
approximately = 14
We should use estimation here as the answer options are not close .(28*10 =280 and 28*20 = 560 , hence we select the only option between 10 and 20 )
Answer C
Answer: C
Question: If -3 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?
Options:
A)-42 < xy < 21
B)-42 < xy < 18
C)-28 < xy < 18
D)-24 < xy < 21
E)-24 < xy < 24
Rationale: The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-3)*(-6)=18.
Therefore -42 < xy < 18.
Answer: B.
Answer: B
Question: If the area of circle is 616 sq cm then its circumference?
Options:
A)76
B)55
C)88
D)21
E)11
Rationale: the area of circle =pie* r^2 = 616 => r = 14
2 * 22/7 * 14 = 88
ANSWER:C
Answer: C
Question: A rectangular plot measuring 30 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
Options:
A)46m
B)66m
C)26m
D)56m
E)32m
Rationale: Perimeter of the plot = 2(30+50) = 160m
no of poles =160/5 =32m
Answer: E
Answer: E
Question: Company X provides bottled water to its employees in 5 liter bottles, $5 each. At least how many 5L bottles must Company X buy monthly, so that new contract with $40 fixed monthly rate and $2 for 20L bottle each paid off? (Assume that no other costs apply)
Options:
A) 4
B) 9
C) 12
D) 20
E) 25
Rationale: let the no. of 5 liter bottles be x, so the no. of 20l bottles will be x/4 (to equate the vol.) since the total cost will be equal , 5x= 40+2*x/4 so x= 8.88 or 9. Answer is (B).
Answer: B
Question: Health insurance Plan V requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A)$600
B)$1000
C)$3800
D)$5300
E)$6200
Rationale: 0.5 * 600 = 300 where V = B.
Answer: B
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)22
B)77
C)36
D)1908
E)21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/15 => x = 30
Speed of each train = 30 m/sec.
= 30 * 18/5 =- 1908 km/hr.Answer: D
Answer: D
Question: 1+2+2^2+2^3+2^4=？
Options:
A)(2^3-1)(2^3+1)
B)2^6+1
C)2^5-1
D)2^5+1
E)2^5-2
Rationale: From 1+2+2^2+2^3+2^4=1(2^5-1)/(2-1)=2^5-1, the correct answer is C.
Answer: C
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is :
Options:
A)A. Rs. 1386
B)B. Rs. 1764
C)C. Rs. 1575
D)D. Rs. 2268
E)None of these
Rationale: Let P.W. be Rs. x. Then, S.I on Rs. X at 16% for 9 months = Rs. 189.
∴ Xx16x 9/12x 1/100 = 189 or x = 1575.
∴ P.W = Rs. 1575.
∴ Sum due =P.W + T.D. = Rs. (1575+189) = Rs. 1764.
Answer B
Answer: B
Question: Each shelf of a bookcase contains 24 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Denoting x the number of the shelves, we can build an equation: 24x=16(x−1)+22+42. Solving the equation, we get x=6
Answer: C
Answer: C
Question: A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be
Options:
A)6
B)9
C)24
D)30
E)35
Rationale: Explanation:
Volume of block=(6 x 9 x 12)cm3 = 648 cm3
Side of largest cube = H.C.F of 6,9,12 = 3cm
Volume of the cube=(3 x 3 x 3)=27 cm3
Number of cubes=(648/27)=24
Answer: C
Answer: C
Question: Machine A and machine B are each used to manufacture 770 sprockets. It takes machine A 10 hours longer to produce 770 sprockets than machine B. Machine B produces 10% more sprockets per hour than machine A. How many sprockets per hour does machineAproduce?
Options:
A)6
B)6.6
C)60
D)100
E)7.7
Rationale: time taken by B = t
time taken by A = t+10
qty produced by A = q
qty produced by B = 1.1 q
for B: t(1.1q) =770
qt=700
for A: (t+10)(q) = 770
qt+10q=770
700+10q=770
q=7
so A can produce 7/hour.
then B can produce = 7(1.1)=7.7/hour.
E
Answer: E
Question: After his first semester in college, Thomas is applying for a scholarship that has a minimum Grade Point Average (GPA) requirement of 3.5. The point values of pertinent college grades are given in the table below. If Thomas took 6 courses, each with an equal weight for GPA calculations, and received two grades of A-, one grade of B+, and one grade of B, what is the lowest grade that Thomas could receive for his fifth class to qualify for the scholarship?
Point Values of Select Grades
Grade: A | A- | B+ | B | B- | C+ | C | C-
Value: 4 | 3.7 | 3.3 | 3 | 2.7 | 2.3 | 2 | 1.7
Options:
A) A
B) B+
C) B
D) B-
E) C+
Rationale: Grade: A | A- | B+ | B | B- | C+ | C | C-
Value: 4 |3.7|3.3|3| 2.7 | 2.3 | 2 | 1.7
7.4 + 3.3 + 3 + x = 3.5 * 5
x = 17.5 - 13.7 = 3.8
Grade A is required to qualify
Answer = A
A
Answer: A
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 45 kms. what was the total distance traveled in 12 hours?
Options:
A)252 kms
B)152 kms
C)672 kms
D)752 kms
E)152 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(45+47+49+.....upto 12 terms)
This is an A.P with first term, a=45, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 45+{12-1) x 2]
=6(112)
= 672 kms.
Answer: C
Answer: C
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)120 m
B)240 m
C)300 m
D)350 m
E)None of these
Rationale: Explanation:
Speed = (54 x5/18)m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then,	x + 300/36 =15
x + 300 = 540
x = 240 m.
ANSWER IS B
Answer: B
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Options:
A)635.50
B)635.53
C)635.57
D)635.52
E)635.51
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer: A
Answer: A
Question: A man brought some eggs of which 10% are rotten. He gives 80% of the remainder to his neighbour. Now he left out with 36 eggs. Hw many eggs he brought
Options:
A)100
B)200
C)72
D)40
E)36
Rationale: Let he bought 100 eggs.
Eggs after removing rotten one = 90.
Eggs given to neighbour = 80% of 90 = 72 eggs.
Now he left with eggs = 90 - 72 = 18 eggs.
Now,
Comparing,
18 = 36
1 = 36/18
ANSWER : OPTION B
100 = 200.
So, he bought 200 eggs.
Answer: B
Question: A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
Options:
A)48 min. past 12.
B)46 min. past 12.
C)45 min. past 12.
D)47 min. past 12.
E)49 min. past 12.
Rationale: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
hrs of this clock = 24 hours of the correct clock.
29 hours of this clock = hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.
Answer:A
Answer: A
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Options:
A)Rs. 1900
B)Rs. 2660
C)Rs. 2800
D)Rs. 2840
E)Rs. 2820
Rationale: For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
B's share = Rs.(7030 x 14/37) = Rs. 2660.
Answer:B
Answer: B
Question: If (5+k)(5-k)=(5^2)-(2^3),then what is the value of K?
Options:
A)1
B)3
C)4
D)2
E)6
Rationale: Obviously,It is in the formula a^2-b^2=(a+b)(a-b)
So k is 2
Option D
Answer: D
Question: The sum of three consecutive multiples of 3 is 108. What is the largest number?
Options:
A)36
B)39
C)33
D)30
E)42
Rationale: Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 108
9x = 99
x = 11
Largest number = 3x + 6 = 39
Answer : B
Answer: B
Question: In 18 minutes, the minute hand gains over the hour hand by
Options:
A)16°
B)80°
C)88°
D)99°
E)110°
Rationale: In one hour, the hour hand moves 30°, which is 0.5° each minute.
In one hour, the minute hand moves 360°, which is 6° each minutes.
The minute hand gains 5.5° each minute.
In 18 minutes, the minute hand gains 18 * 5.5° = 99°.
The answer is D.
Answer: D
Question: The roof of an apartment building is rectangular and its length is 7 times longer than its width. If the area of the roof is 847 feet squared, what is the difference between the length and the width of the roof?
Options:
A)38.
B)40.
C)66.
D)44.
E)46.
Rationale: Answer is C : 66
Let w be the width , so length is 7w. Therefore : w*7w = 847, solving for, w = 11 , so 7w-w =6w = 6*11 = 66
Answer: C
Question: P, Q and R have $6000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options:
A)2400
B)2403
C)3998
D)2539
E)1930
Rationale: A
2400
Let the amount with R be $ r
r = 2/3 (total amount with P and Q)
r = 2/3(6000 - r) => 3r = 12000 - 2r
=> 5r = 12000 => r = 2400.
Answer: A
Question: A(3, w^3) is the (x, y) coordinate of point located on the parabola Y = X^2 -1. What is the value of w?
Options:
A)2.
B)4.
C)5.
D)6.
E)9.
Rationale: y=x^2 - 1
w^3=3^2-1
w^3=8
W=2
Answer A
Answer: A
Question: R is a positive integer and 225 and 216 are both divisors of R. If R=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?
Options:
A)8
B)5
C)6
D)7
E)4
Rationale: Lets make factorization of 225 and 216 ..
225 = 5 X 5 X 3 X 3 X 3
216 = 2 X 2 X 2 X 3 X 3 X 3
R would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2 = 8(A) (answer) ...
Answer: A
Question: Which one of the following can't be the square of natural number ?
Options:
A)20164
B)32761
C)42437
D)81225
E)None of these
Rationale: The square of a natural number never ends in 7.
42437 is not the square of a natural number.
ANSWER :C
Answer: C
Question: 5358 x 52 = ?
Options:
A)272258
B)272358
C)278616
D)274258
E)274358
Rationale: 5358 x 51	= 5358 x (50 + 2)
= 5358 x 50 + 5358 x 2
= 267900 + 10716
= 278616.
C)
Answer: C
Question: The greatest common factor of two numbers is 5!. Which of the following can be the second number, if one of the numbers is 7!?
Options:
A)3(5!)
B)4(5!)
C)6(5!)
D)5(5!)
E)7(5!)
Rationale: GCF is the product of common factors of the numbers involved.
GCF = 5!
a = 7! = 7*6*5!
b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)
Looking at the answers only 5 (5!) and 7! will have GCF as 5!
Ans D
Answer: D
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)2 : 8
B)2 : 9
C)2 : 5
D)2 : 4
E)2 : 2
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5.Answer: C
Answer: C
Question: If an integer e is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that e(e + 1)(e + 2) will be divisible by 8?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: for e Total numbers 8*12
There are 12 numbers divisible by 8 -> 3*12 (if 8 is an example - (6,7,8), (7,8,9), (8,9,10))
and 12 numbers divisible by 4 but not divisible by 8 -> 2*12 (if 4 is an example (2,3,4) and (4,5,6))
The answer 5/8 -> D
Answer: D
Question: During a Pizza buffet where A eats more times 2.6 than B, and B eats 4 times less than C.find the least number of times all the three has to eat
Options:
A)250
B)260
C)270
D)280
E)285
Rationale: A eats more than B if B eats 1 times than the ratio of A and B is A:B is 2.6:1 or 13:5 and as B eat 4 times less the C the the ratio of B : C is 5:20 the the least number of times all three has eat is the LCM of A,B,C that is 260 ..
ANSWER:B
Answer: B
Question: One side of rectangular field is 15 meter and one of its diagonals is 17 meter. Then find the area of the field.
Options:
A)120m2
B)130m2
C)140m2
D)150m2
E)160m2
Rationale: Explanation:
We know h2=b2+h2
=>Other side
=√(17)2−(15)2
=√289−225
=√64
=√8meter
Area=Length×Breadth
=15×8m2=120m2
ANSWER IS A
Answer: A
Question: A bowl was filled with 5 ounces of milk, and 0.0025 ounce of the milk evaporated each day during a 30-day period. What percent of the original amount of milk evaporated during this period?
Options:
A)A)0.0015%
B)B)0.015%
C)C)1.5%
D)D)150%
E)E)1500%
Rationale: Total amount of milk evaporated each day during a 30-day period = .0025 * 30
=.0025 * 30
= .075
percent of the original amount of milk evaporated during this period = (.075/5) * 100%
= 1.5 %
Answer C
Answer: C
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:14. If P invested the money for 5 months, find for how much time did Q invest the money?
Options:
A)19
B)14
C)13
D)10
E)12
Rationale: 7*5: 5*x = 7:14
x = 14
Answer: B
Answer: B
Question: The difference between a two digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
Options:
A)2
B)3
C)4
D)8
E)9
Rationale: Solution
Let the ten's digit be x and units digit be y.
Then, (10x+y) - (10y+x)= 36	‹=›9(x - y) = 36
‹=›x - y = 4.
Answer C
Answer: C