divelab/Sys2Bench huggingface dataset:
Question: If the volume of two cubes are in the ratio 64:1, the ratio of their edges is:
Options:
A)3:1
B)3:2
C)3:5
D)4:1
E)None of these
Rationale: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=64/1
=>(a/b)3=(4/1)3
a/b=4/1
=>a:b=4:1
Option D
Answer: D
Question: If p and q are prime numbers, how many divisors does the product p^4 * q^9 have?
Options:
A)30
B)35
C)40
D)50
E)60
Rationale: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)
Therefore, the answer is D. 5*10=50
Answer: D
Question: Three positive integers a, b, and c are such that their average is 20 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: Solution:
We know that the average value is 20 therefore (a+b+c)/3 = 20
so a+b+c = 60
and b = a + 13
therefore a + (a + 13) + c = 60
The least value of c is when c = b
so take c = a + 13
hence, a + (a + 13) + (a + 13) = 60
i.e., a = 34/3 a non integer therefore c is not equal to b
so take c = b+1 therefore c = a+14
a + (a + 13) + (a + 14) = 60
i.e., a= 33/3 = 11
hence, a = 11, b = 24, and c = 25
Answer: E
Answer: E
Question: The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by
14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6.
Options:
A)1396
B)1394
C)1494
D)1384
E)1391
Rationale: The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by
14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6.
= 1400-6 = 1394
Answer is B
Answer: B
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour and $.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $800 (before payroll deductions)?
Options:
A)1800
B)1825
C)1850
D)1855
E)1875
Rationale: Hourly = $12.50/hour
TotalHours = 40
PieceWork = $0.16/widget
TotalPieces = ????
Total Pay = (Hourly * TotalHours) + (PieceWork * TotalPieces)
so, put it all together:
$800 = ($12.50 * 40) + ($0.16 * Total Pieces)
TotalPieces = ($800 - ($12.50*40)) / $0.16 = 1875 Widgets
E. 1875
Answer: E
Question: A certain sum of money at simple interest amounted Rs.680 in 8 years at 3% per annum, find the sum?
Options:
A)548
B)675
C)588
D)678
E)989
Rationale: 680 = P [1 + (8*3)/100]
P = 548
Answer: C
Answer: C
Question: Find the odd man out
1, 2, 5, 14, 41, 123
Options:
A)2
B)14
C)124
D)123
E)21
Rationale: 1*3-1 =2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3 -1 = 122
ANSWER:D
Answer: D
Question: What is the value of (P + Q)/(P - Q) if P/Q is 7?
Options:
A)4/3
B)2/3
C)2/6
D)7/8
E)8/7
Rationale: (P + Q)/(P - Q) = [(P/Q) + 1]/[(P/Q) - 1]
= (7 + 1)/(7 - 1)
= 8/6
= 4/3
ANSWER:A
Answer: A
Question: A car traveling at a certain constant speed takes 5 seconds longer to travel 1 km than it would take to travel 1 km at 75 km/hour. At what speed, in km/hr, is the car traveling?
Options:
A)70
B)72
C)74
D)75
E)78
Rationale: Time to cover 1 kilometer at 80 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds;
Time to cover 1 kilometer at regular speed is 48 + 5 = 53 seconds = 53/3,600 hours = 1/70 hours;
So, we get that to cover 1 kilometer 1/70 hours is needed --> regular speed 70 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: A
Answer: A
Question: A train 120 m long is running with a speed of 62 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going
Options:
A)5 sec
B)6 sec
C)7 sec
D)8 sec
E)9 sec
Rationale: Explanation:
Speed of the train relative to man = (62 - 8) kmph
= (54× 5/18) m/sec = 15 m/sec
Time taken by the train to cross the man
= Time taken by It to cover 120 m at 15m / sec
= 120 ×1/15 sec = 8sec
Answer: Option D
Answer: D
Question: A mixture contains milk and water in the ratio 6:3. On adding 10 litters of water, the ratio of milk to water becomes 6:5. The quantity of milk in the original mixture is?
Options:
A)90
B)45
C)110
D)40
E)50
Rationale: Explanation:
milk:water = 6:3
6x : 3x + 10 = 6 : 5
5[6x] = 6[3x + 10]
30x = 18x + 60
30x - 18x = 60
12x = 60
x = 5
The quantity of milk in the original mixture is = 6 : 3 = 6 + 3 = 9
9x = 45
Short cut method - 2 : for Only milk problems
milk : water
6 : 3
6 : 5
milk ratio same but water ratio 2 part incress per 10 liters
2 part of ratio -------> 10 liters
9part of ratio -------> 45 liters
Answer: Option B
Answer: B
Question: The average of 9 numbers is 7 and the average of 7 other numbers is 10. What is the average of all 16 numbers?
Options:
A)9
B)8 5/16
C)7 7⁄8
D)7 1⁄2
E)7 1⁄4
Rationale: The average of 9 numbers is 7....
The sum of those numbers is (9)(7) = 63.
The average of 7 other numbers is 10....
The sum of those numbers is (7)(10) = 70
The sum of ALL 16 numbers is 63+70 = 133. The average of those numbers is 133/16 = 8 5/16.
Final Answer:
[Reveal]Spoiler:
B
Answer: B
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?
Options:
A)8867
B)299
C)279
D)600
E)2612
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1500
=> 5 parts out of 15 parts is Rs. 1500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1500) = Rs. 600.Answer: D
Answer: D
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8300. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Options:
A)2177
B)2876
C)4500
D)5300
E)6711
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8300 = 33200 ----(2)
(2)-(1) i.e. May - Jan = 1200
Salary of May is Rs.6500
Salary of January = Rs.5300.Answer: D
Answer: D
Question: What is the product of all the prime factors of 24?
Options:
A)36
B)24
C)48
D)12
E)6
Rationale: 24 , factors are 2,3,4,8,6,12. Now again prime Numbers are Only Two i.e 2 and 3 , this time we would have 2*2*2*3=24
Answer : B
Answer: B
Question: Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ?
Options:
A)0
B)3
C)4
D)5
E)6
Rationale: Explanation :
p + q = α –2 and pq = –α – 1
(p + q)2 = p2 + q2 + 2pq,
Thus (α –2)2 = p2 + q2 + 2(–α – 1)
p2 + q2 = α2 – 4α + 4 + 2α + 2
p2 + q2 = α2 – 2α + 6
p2 + q2 = α2 – 2α + 1 + 5
p2 + q2 = (α – 1)2 + 5
Thus, minimum value of p2 + q2 is 5.
Answer : D
Answer: D
Question: what is the Max number of rectangular boxes, each measuring 5 inches by 2 inches by 7 inches, that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches, if all boxes are aligned in the same direction?
Options:
A)200
B)350
C)100
D)150
E)120
Rationale: The 5 inch side should be aligned to the 15 inch side ( 3 layer)
2 inch side should be aligned to the 20 inch side. (10 layer)
7 inch side should be aligned to the 35 inch side.(5 layer)
Maximum number of rectangles =3*10*5=150
Answer is D
Answer: D
Question: When a number is divided by 6 &then multiply by 12 the answer is 10 what is the no.?
Options:
A)4.5
B)5
C)5.6
D)5.7
E)6.5
Rationale: if $x$ is the number, x/6 * 12 = 10
=> 2x = 10
=> x = 5
B
Answer: B
Question: In a group of 80 children and 10 youngsters, each child got sweets that are 20% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
Options:
A)1140
B)1160
C)1280
D)1200
E)1210
Rationale: Number of sweets each child got = 20% of 80 = 20/100 * 80 = 16.
Number of sweets 80 children got = 80 * 16 = 1080.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 10 * 20 = 200.
Total number of sweets = 1080 + 200 = 1280.
C)
Answer: C
Question: The average marks of a class of 22 students is 40 and that of another class of 28 students is 60. Find the average marks of all the students?
Options:
A)51.2
B)59.5
C)52.8
D)52.5
E)52.1
Rationale: Sum of the marks for the class of 22 students = 22 * 40 = 880
Sum of the marks for the class of 28 students = 28 * 60 = 1680
Sum of the marks for the class of 50 students =
880 + 1680 = 2560
Average marks of all the students = 2560/50
= 51.2
Answer:A
Answer: A
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE?
Options:
A)94
B)113
C)114
D)121
E)123
Rationale: Total no'of arrangements 5P5 = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114
C)
Answer: C
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
Options:
A)18
B)77
C)32 days
D)16
E)12
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer: C
Answer: C
Question: If the probability of rain on any given day in City X is 50%, what is probability that it rains on exactly 4 days in a 5 day period?
Options:
A)2/5
B)4/5
C)3/16
D)4/32
E)5/32
Rationale: One possible way is rain-rain-rain-rain-no rain.
The probability of this is 1/2*1/2*1/2*1/2*1/2 = 1/32
The number of possible ways is 5C4 = 5, so we multiply this by 5.
P(rain on exactly 4 days) = 5*1/32 = 5/32
The answer is E.
Answer: E
Question: Running 3/4th of his usual rate, a man is 12min late. Find his usual time in hours ?
Options:
A)6/4 hrs
B)3/5 hrs
C)9/4 hrs
D)3/4 hrs
E)1/4 hrs
Rationale: Explanation:
Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time
so 1/3rd of the usual time = 12min
or usual time = 3 x 12 = 36min = 36/60 hrs = 3/5 hrs.
Answer: B
Answer: B
Question: A sum of Rs. 125000 amounts to Rs. 15500 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)7%
B)9%
C)5%
D)6%
E)2%
Rationale: S.I. = (15500 - 12500) = Rs. 3000\
Rate = (100 * 3000) / (12500 * 4)
= 6%
Answer: D
Answer: D
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.36, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.]
Options:
A) 0.33
B) 0.44
C) 0.48
D) 44
E) 48
Rationale: A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 36 cents;
A half-liter of kerosene costs as much as 8 eggs --> 8 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 16 eggs = 16/12*36 = 48 cents.
Answer: E.
Answer: E
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits M of the larger integer?
Options:
A)M=2
B)M=5
C)M=8
D)10
E)11
Rationale: Really hard. But let's start with few concepts:
1. Square of an odd integer will be odd.
2. Difference of odd and odd will be even.
3. Any odd integer can be expressed as difference of two squares.
4. An even integer can be expressed as difference of two squares only if that even integer is a multiple of 4.
Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that itcompletesa perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: A
Question: How many three digit numbers that do not contain the digit 9 are there?
Options:
A)100
B)200
C)512
D)596
E)648
Rationale: Applying combinations....8 * 9 * 9 = 648...
8 for first digit...cant be 0 or 9
9 and 9 for 2nd and 3rd....cant be 9
ANSWER: E
Answer: E
Question: The difference between a number and its three-fifth is 50. What is the number?
Options:
A)185
B)190
C)160
D)120
E)125
Rationale: Let the number be x. Then,
x - 3/5 x = 50 => 2/5 x = 50
x = (50 * 5)/2 = 125.
ANSWER: E
Answer: E
Question: One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field in meter square
Options:
A)100
B)110
C)120
D)130
E)140
Rationale: Other side = ((17) 2- (15)2)(1/2)
= (289- 225)(1/2)
= (64)(1/2)
= 8 m.
Area = (15 x 8) m2 = 120 m2.
Option C
Answer: C
Question: A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability E that both will be juniors?
Options:
A)1/10
B)1/5
C)2/9
D)2/5
E)1/2
Rationale: I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.
2 seniors = P(Senior) * P(Senior) = 2/9
1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9
Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability E that it is two juniors is 1- (7/9) = 2/9.C
Answer: C
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Options:
A)26
B)32
C)72
D)88
E)82
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
Answer: B
Answer: B
Question: A rectangular tiled patio is composed of 126 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 126 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
Options:
A)5
B)6
C)9
D)13
E)28
Rationale: Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 126
Also. Reach column has r tiles and each row has c tiles
New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 126
Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c*r=126
(2r-4)*r = 126
2r^2 - 4r - 126=0
r cannot be negative so r = 9
and c = 14
So, Answer will be C
Answer: C
Question: Two numbers are in the ratio of 3:8. If 24 be subtracted from each, they are in the ratio of 4:9. Find the numbers?
Options:
A)60,89
B)60,88
C)-27,-128
D)60,84
E)-72,-192
Rationale: (3x-24):(8x-24) = 4:9
x = -24=> -72,-192
Answer: E
Answer: E
Question: Which of the following is closest to (-6/7)^199？
Options:
A)-1
B)-1/2
C)0
D)1
E)2
Rationale: (-6/7)^4 = 1296/2401 which is already close to 1/2.
For larger exponents, the expression will get closer and closer to zero.
The answer is C.
Answer: C
Question: In a partnership between A, B and C. A's capital is Rs.8000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)23676
B)19766
C)29172
D)18800
E)11267
Rationale: Explanation:
200 + 130 = 330
800 - 330 = 470
200 ---- 8000
470 ---- ? => 18800
Answer:D
Answer: D
Question: If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4340 , R will receive
Options:
A)600
B)700
C)840
D)900
E)None of these
Rationale: Explanation :
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4340 * (6/31) = 140*6 = 840. Answer : Option C
Answer: C
Question: If w and b are positive numbers, and w^3 + b^3 = 75, then the greatest possible value of w is between:
Options:
A)0 and 3
B)3 and 5
C)4 and 5
D)5 and 7
E)6 and 9
Rationale: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .
The question stated: w and b are positive numbers but not positive integers.
so fractions are allowed to be a part of calculation.
So if the answer is C then the value 4.5 = 9/2 must comply the equation.
(9/2)^3 + b^3 = 75
so, b^3 = -129/8 , which is not possible according to the question.
Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .
hi asif,
question is correct IMO.
Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation
question is asking that maximum value ofa(means that unique value ofa) is between...
its not saying all value of that range will satisfy.
Answer: C
Question: Peter's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the Peter's average score on the 5 tests to be 80?
Options:
A) 80
B) 82
C) 84
D) 86
E) 88
Rationale: E. 88
Peter must score at least an 80 for sure. If he scores an 8, then he will need to score 2 pots for each of the 4 other tests tomake upthe difference. They each were at 78 (at least the average is, but this is a small point and doesn't matter to the answer). So 4 tests that were each 2 points short of the 80 average that is desired means the next test must be 8 points higher than the desired average, so 80+8 = 88.
Answer: E
Question: When 75% of a number is added to 75, the result is the same number. The number is
Options:
A)150
B)150
C)100
D)450
E)None of these
Rationale: Let the number be equal to x.
3x/4 +75 = x
Hence x=300
Answer: B.
Answer: B
Question: Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week?
Options:
A)Rs.150
B)Rs.190
C)Rs.200
D)Rs.250
E)Rs.300
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
D)
Answer: D
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)10%
B)12%
C)14%
D)20%
E)22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
B)
Answer: B
Question: Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 80 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?
Options:
A)70 miles
B)80 miles
C)90 miles
D)100 miles
E)110 miles
Rationale: Every hour, Nil gets ahead of Ethan 80 - 20 =
60 miles. When Nil arrived at the beach, Ethan
is only 20 × 0.5 = 10 miles behind. That tells us
they only drove 1 hour when Nil arrived at the
beach.
The distance between their home and the beach
is
Nil’s speed × Nil’s time
= 80 × 1 = 80 miles.
correct answer B
Answer: B
Question: Solve the equation for x : 6x - 87 + 3x = 4 + 9 - x
Options:
A)12
B)5
C)10
D)9
E)3
Rationale: C
10
9 x + x = 13 + 87
10 x = 100 => x = 10
Answer: C
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
Options:
A)300 kmph
B)360 kmph
C)600 kmph
D)720 kmph
E)750 kmph
Rationale: Explanation:
Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr.
Required speed =(1200 X 3/5)km/hr	= 720 km/hr.
ANSWER IS D
Answer: D
Question: The sum P of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Pn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
Options:
A)4345
B)4302
C)4258
D)4214
E)4170
Rationale: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit as we have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum P of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Answer: D
Question: If each year the population of the country grows by 30%, how many years will elapse before the population of the country doubles?
Options:
A)2
B)4
C)5
D)3
E)7
Rationale: Till Year 2000, population is 100 .
Year 2001: Population becomes 130 ............. 1 Year elapsed
Year 2002: Population becomes 169 ............. 2 Year elapsed
Year 2004: Population > 200 .................. 3 year elapsed
Answer:D
Answer: D
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)Rs.1014
B)Rs.1140
C)Rs.999
D)Rs.1085
E)Rs.1020
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999
ANSWER:C
Answer: C
Question: John read the quarter of the time that Tom read. Tom read only two-fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read?
Options:
A)2 hours
B)4 hours
C)1 hours
D)5 hours
E)7 hours
Rationale: Mike read 5 hours. Sasha read twice as long as Mike. Hence Sasha read:
2 * 5 = 10 hours
Tom read two-fifths of the time that Sasha read. Hence Tom read:
(2 / 5) * 10 = 4 hours
John read the quarter of the time that Tom read. Hence John read:
(1 / 4) * 4 = 1 hour
correct answer C
Answer: C
Question: The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
Options:
A)21:29
B)21:27
C)21:22
D)21:23
E)21:21
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
i.e., (120/100 * 7x) and (110/100 * 8x)
i.e., 42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer: C
Answer: C
Question: Given a certain positive integer X, if x is divided by 5 the remainder is 3 and if it is divided by 7 the remainder is 5. What is the remainder when x is divided by 30.
Options:
A)5
B)Between 1 and 4, inclusive
C)Between 5 and 10, inclusive
D)Between 10 and 12, inclusive
E)above 12
Rationale: Put in real numbers.
Given number x
5x+3 = 7x+5
Start 5x+3 --> 8, 13, 18, 23, 28, 33,....
Of these only 33 fit the description 7x+5. The remainder when divided by 30 is 3. So answer is B).
If there is a purely algebraic way, please tell.
Answer = B)
Answer: B