divelab/Sys2Bench huggingface dataset:
Question: The difference between two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is :
Options:
A)240
B)270
C)295
D)360
E)None
Rationale: Solution
Let the numbers be x and (x + 1365).
Then, x + 1365 = 6x + 15 ⇔ 5x = 1350 ⇔ x = 270.
Answer B
Answer: B
Question: 16,25,36,72,144,196,225
Options:
A)36
B)196
C)225
D)144
E)72
Rationale: Each of the numbers except 72 is a perfect square.
answer :E
Answer: E
Question: Of the 3,600 employees of Company X, 12/25 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
Options:
A)40%
B)22.2%
C)20%
D)12.5%
E)11.1%
Rationale: Let's see, the way I did it was
12/25 are clerical out of 3600 so 1728 are clerical
1728 reduced by 1/4 is 1728*1/4
so it reduced 432 people , so there is 1296 clerical people left
but since 432 people left, it also reduced from the total of 3600 so there are 3168 people total
since 1296 clerical left / 3168 people total
you get (A) 40%
Answer: A
Question: Train W leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?
Options:
A)8:15 am
B)8:45 am
C)9:00 am
D)9:30 am
E)Cannot be determined from the information given
Rationale: train W will cover 60 kms in 45 min at 7:45, the time when train B starts...
distance left to cover is 210-60=150..
combined speed=80+70=150..
so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45
B
Answer: B
Question: A car covers a distance of 10km in 12 minutes. If its speed is decreased by 5km/hr, the time taken by the car to cover the same distance will be?
Options:
A)10min 12sec
B)15min 45sec
C)13min 20sec
D)20min 4sec
E)30min 13sec
Rationale: Speed = 10*60/12 = 50km/hr
New speed = 50-5 = 45 km/hr
Time taken = 10/45 = 60*2/9 = 13min 20sec
Answer is C
Answer: C
Question: Two cars cover the same distance at the speed of 50 and 62 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
Options:
A)250 km
B)214 km
C)224 km
D)216 km
E)204 km
Rationale: 50(x + 1) = 62x
X = 4.16
60 * 4.16 = 250 km
ANSWER:A
Answer: A
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
Options:
A)289
B)269
C)207
D)480
E)271
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
Answer: D
Answer: D
Question: A man walking at the speed of 4 kmph crosses a square field diagonally in 3 minutes. The area of the field is:
Options:
A)18000m2
B)20000m2
C)19000m2
D)25000m2
E)15000m2
Rationale: Length of the diagonal= Distance covered in 3 min. at 4 km/hr.
= (4000/ 60 *3)= 200m.
Therefore, Area of the field= 1/2 * diagonal2
= ½ * 200*200 = 20000 m2
ANSWER:B
Answer: B
Question: During 2003, a company produced an average of 1,000 products per month. How many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 200% over its 2003 average?
Options:
A)132,000
B)235,000
C)175,000
D)200,000
E)250,000
Rationale: Company produced 12*1000 = 12,000 products in 2003. If company produces X products from 2004 to 2007, then total amount of product produced in 4 years (2003 through 2007) is X+12,000. The gives the average of (X+12,000)/4.
This average needs to be 200% higher than that in 2003. In math terms, 12,000+200%(12,000) = 36,000. So:
(X+12,000)/4 = 36,000
X+12,000 = 144,000
X = 132,000
The answer is A.
Answer: A
Question: Of the families in City X in 1992, 60 percent owned a personal computer. The number of families in City X owning a computer in 1993 was 50 percent greater than it was in 1992, and the total number of families in City X was 3 percent greater in 1993 than it was in 1992. what percent of the families in City X owned a personal computer in 1993?
Options:
A)68.99%
B)66.55%
C)91.23%
D)77.77%
E)87.37%
Rationale: Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 60
Number of families owning computer in 1998 = 60 * 150/100 = 90
Number of families in 1998 = 103
The percentage = 90/103 * 100 = 87.37%.
ANSWER:E
Answer: E
Question: In digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be?
Options:
A)3387
B)1000
C)2866
D)2787
E)1121
Rationale: 20 * 10 * 5 = 1000
Answer: B
Answer: B
Question: If b does not equal zero, and ab = b/5, what is the value of a?
Options:
A)A)1/5
B)B)1/4
C)C)1/3
D)D)1/2
E)of the above
Rationale: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/5
(ab)/b = (b/5)/b
a = (b/5)*1/b
a = 1/5
Answer: (A).
Answer: A
Question: 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively
Options:
A)7 and 4
B)7 and 5
C)8 and 4
D)8 and 5
E)None
Rationale: Let the given number be 476 xy 0.
Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.
And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.
x - y - 3 = 0 y = x - 3
(17 + x + y) = (17 + x + x - 3) = (2x + 14)
x= 2 or x = 8.
x = 8 and y = 5.
Option D
Answer: D
Question: In a class of 69 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
Options:
A)6
B)15
C)24
D)33
E)54
Rationale: Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total
so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 69
54 + NOT = 69
NOT = 69 - 54 = 15
So answer is B
Answer: B
Question: Find the simple interest on $3000 for 3 years at 10% per annum?
Options:
A)$900
B)$300
C)$500
D)$600
E)$1000
Rationale: SI = PTR/100
= 3000*3*10/100 = $900
Answer is A
Answer: A
Question: How many different positive integers are factors of 36 ?
Options:
A)10
B)2
C)7
D)3
E)2
Rationale: 36=2*18
3*12
4*9
6*6
Answer : C
Answer: C
Question: A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 10% p.a. for the same time period. Therefore the interest received is more by Rs. 840. Find the sum?
Options:
A)s. 8400
B)s. 9000
C)s. 14000
D)s. 17000
E)s. 27000
Rationale: Let the sum be Rs. x.
(x * 15 * 2)/100 - (x * 10 * 2)/100 = 840
=> 30x/100 - 20x/100 =840
=> 10x/100 = 840
=> x = 8400.
ANSWER:A
Answer: A
Question: Car Z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
Options:
A)320
B)384
C)400
D)408.3
E)440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 45 miles/hour, the car will run 48 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 38.4 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 38.4 miles/gallon * 10 gallons = 384 miles.
Answer B.
Answer: B
Question: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
Options:
A)5
B)8
C)15
D)20
E)25
Rationale: Use the forumla ;
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
100 = 50 + 30 + 20 - ( sum of 2) -2(7) +15
100 = 101-( sum of 2)
1 = sum of 2
so more than 1 = 8
B
Answer: B
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
Options:
A)81:121
B)81:128
C)81:126
D)81:124
E)81:122
Rationale: Ratio of the sides = ³√729 : ³√1331
= 9 : 11
Ratio of surface areas = 92 : 112
= 81:121
Answer: A
Answer: A
Question: Which of the following points is closest to line y=x
Options:
A)(2, -1)
B)(2, 4)
C)(1, 1)
D)(2, -1)
E)(-2, 0)
Rationale: Attachment:
m12-20.pngAs you can see point (1, 1) is the closest to line y=x.
Answer: C.
Answer: C
Question: x and y are positive integers. If x is a prime factor of y^2 , which of the following MUST be true?
Options:
A)x is even
B)x=y^2
C)y/x is even
D)x/y <=1
E)x+1 is also the prime factor of y^2
Rationale: A. x is even --> not necessarily true: x=3=odd and y=3
B. x=y2--> never true, as x=primex=prime then it can not equal to square of another integer;
C. yx is even --> not necessarily true: if x=3x=3 and y=3y=3 then yx=1=odd
D. xy≤1 is less than or equal to 1 --> always true as shown above or by POE;
E. x+1 is also a prime factor of y2--> not necessarily true: if x=2 and y=2 then x+1=3 and 3 is not a factor of y2=4
Answer: D.
Answer: D
Question: How many numbers with 2 different digits can be formed using only the odd digits?
Options:
A)10
B)20
C)40
D)60
E)120
Rationale: Odd digits are 1, 3, 5, 7, 9.
We want 3 different digits.
First digit can be chosen in 5 ways.
Second digit can be chosen in 4 ways.
Total ways = 5*4
= 20
Hence option (B).
Answer: B
Question: What is the least number of digits (including repetitions) needed to express 10^600 in decimal notation?
Options:
A)a) 4
B)b) 601
C)c) 101
D)d) 1000
E)e) 1001
Rationale: 10^n is a decimal number with a 1 followed by n zeros.
So 10^600 will include 600 0's + 1 digit for 1 = 601
So the answer is B
Answer: B
Question: In a 2000 m race, A beats B by 100 meters or 40 seconds. Find the speed of B?
Options:
A)10m/s
B)2.5m/s
C)5m/s
D)7m/s
E)3m/s
Rationale: Since A beats B by 100 m or 40 seconds,
it implies that B covers 100 m in 40 seconds.
Hence speed of B = 100/40 = 2.5 m/s.
Answer: B
Answer: B
Question: It takes 2 tons of copper ore and 4 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?
Options:
A) 18
B) 18 3/4
C) 20
D) 22 1/2
E) 50
Rationale: Yes, you need copper ore:iron ore in the ratio 2:4. Total 6 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 60 tons of copper ore, it is enough for 60/2 = 30 tons of alloy A.
If you have 90 tons of iron ore, it is enough for 90/4 = 22 1/2 tons of alloy A.
Since iron ore is available for only 22 1/2 tons of alloy A, you can make only 22 1/2 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.
Answer must be 22 1/2.
(D)
Answer: D
Question: If a fair coin is flipped seven times in a row, what is the probability that there will be at least one head and one tail?
Options:
A)3/4
B)11/12
C)15/16
D)31/32
E)63/64
Rationale: The number of possible outcomes is 2^7 = 128
There is one way to get no heads and one way to get no tails.
Thus there are 126 outcomes with at least one head and one tail.
P(at least one head and one tail) = 126/128 = 63/64
The answer is E.
Answer: E
Question: A watch was sold at a loss of 10%. If it was sold for Rs.196 more, there would have been a gain of 4%. What is the cost price?
Options:
A)s:1000
B)s:1067
C)s:1278
D)s:1028
E)s:1400
Rationale: 90%
104%
--------
14% ---- 196
100% ---- ? =>
Rs:1400
Answer: E
Answer: E
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 12 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
Options:
A)4 DAYS
B)6 DAYS
C)8 DAYS
D)18 DAYS
E)NONE OF THESE
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/6, B'S 1 DAY'S WORK = 1/12
(A+B)'S 1 DAY'S WORK = (1/6+1/12)=3/12=1/4
SO, A AND B TOGETHER CAN FINISH THE WORK IN 4 DAYS.
CORRECT OPTION: A
Answer: A
Question: John traveled 80% of the way from Yellow-town to Green-fields by train at an average speed of 80 miles per hour. The rest of the way John traveled by car at an average speed of v miles per hour. If the average speed for the entire trip was 70 miles per hour, what is v in miles per hour?
Options:
A)30
B)40
C)50
D)55
E)60
Rationale: HiBunuel
THe question seems incorrect. it should not be 80% at the speed of 80. However if it's 20% at the speed of 80, Answer comes out 55.
The question is correct. Here's the explanation:
Let distance be D. We can find the total timeequate it, which comes as:
0.8D / 80 + 0.2D / v = D / 70 => v = 60 (Option E).
Answer: E
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4000, what will be the difference between Q and R's share?
Options:
A)2788
B)5000
C)7282
D)2782
E)2729
Rationale: 4 --- 4000
5 --- ? => 5000
Answer:B
Answer: B
Question: In the next Worldcup of cricket there will be 12 teams, divided equally in 2groups. Teams of eachgroup will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. 4top teams of this round will qualify for the semifinal round, where they play the best of 3matches. The Minimum number of matches in the next World cup will be
Options:
A)48
B)49
C)53
D)55
E)58
Rationale: The number of matches in first round,
= 6C2 +6C2;
Number of matches in next round,
= 6C2;
Number of matches in semifinals,
= 4C2;
Total number of matches,
= 6C2 +6C2+6C2+4C2+2.
= 53.
C
Answer: C
Question: find the number, difference between number and its 3/5 is 62.
Options:
A)150
B)153
C)154
D)155
E)156
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 62,
=> (2/5)x = 62 => 2x = 62*5,
=> x = 155
Answer: Option D
Answer: D
Question: A team bought a total of 198 balls. If each player on the team bought at least 17 balls, then what is the greatest possible number of players on the team?
Options:
A)21
B)11
C)23
D)24
E)25
Rationale: 198/17=11 plus remainder.
The answer is B.
Answer: B
Question: Every month Rani gives 65% of her salary to her mother. She spends 15% of her salary and saves the remainder. She saves $130 more than what she spends. What is her monthly salary?
Options:
A)2200
B)2400
C)2600
D)2800
E)3000
Rationale: Total Salary given+Spent+Saving= 100%
65%+15%+Savings =100%
80%+Savings=100%
Savings=100%-80%=20%
Savings%-Spent%=$130
20-15=5%
5%of Salary =$130
5/100 * Salary = 130
Salary =130*100/5 =$2600
answer : C
Answer: C
Question: If you select two cards from a pile of cards numbered 1 to 10, what is the probability that the sum of the numbers is less than 4?
Options:
A)1/45
B)4/45
C)1/15
D)1/10
E)1/5
Rationale: The number of ways to choose two cards is 10C2=45.
There is only one way to get a sum less than 4.
P(sum less than 4)=1/45
The answer is A.
Answer: A
Question: The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was 22. Find the amount of the bill.
Options:
A)1,100
B)200
C)2,200
D)Data inadequate
E)None of these
Rationale: Successive discount = 20%+20×80/100
= 20 + 16 = 36%
Difference in discount = 36 – 35 = 1%
\ Bill amount = 22 × 100 = 2200
Answer C
Answer: C
Question: A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?
Options:
A)3 km
B)2 km
C)8 km
D)6 km
E)9 km
Rationale: D
Average speed = (2 * 3 * 2) / (3 + 2) = 12/5 km/hr.
Distance traveled = 12/5 * 5 = 12 km.
Distance between house and school = 12/2 = 6 km.
Answer: D
Question: Rahim bought 27 books for Rs.581 from one shop and 20 books for Rs.594 from another. What is the average price he paid per book ?
Options:
A)28
B)18
C)27
D)25
E)21
Rationale: Average price per book
= (581+ 594) / (27 + 20)
= 1175 / 47
= Rs.25
Answer:D
Answer: D
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)22
B)10
C)88
D)566
E)222
Rationale: 4/12 + x/15 = 1
x = 10.Answer: B
Answer: B
Question: In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
Options:
A)L(L-N) / L-M
B)L(N-M) / L-M
C)L-N
D)M-N
E)M+
Rationale: the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 300
M = 10
N =20.
So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, leaving us with just ..A
Out of which, i choose A.
Answer: A
Question: By selling 16 pencils for a rupee a man loses 5%. How many for a rupee should he sell in order to gain 15%?
Options:
A)12.95
B)19
C)17.56
D)16.56
E)15
Rationale: 85% --- 16
105% --- ?
85/105 * 16 = 8
Answer: A
Answer: A
Question: Four friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 4-person seating arrangements are possible?
Options:
A)6
B)8
C)10
D)12
E)24
Rationale: The number of ways to arrange 4 people in a row is 4!
From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 2 other friends is 3! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 4 friends with the 2-person unit together is 3!*2
The total number of permutations where these two friends are not seated next to each other is 4! - 3!*2 = 24-12 = 12
The answer is D.
Answer: D
Question: Tough and Tricky questions: Exponents.
If 2^(3x+2)*3^(2y-3) = 32^x*9^y, then x + y =
Options:
A)-3
B)-1
C)0
D)-5
E)-2
Rationale: Here is my solution.
2^(3x+2)*3^(y-3) = 32^x*9^y
Here RHS 32^x*9^y= 2^(5x)*3^(2y)
Equating powers on both sides-->
3x+2=5x , thus x=1 and
y-3=2y giving y=-3
So, x+y=-2
Option: E
Answer: E
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament.
How many matches were played?
Options:
A)99 matches.
B)88 matches.
C)77 matches.
D)66 matches.
E)119 matches.
Rationale: Solution:
119 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played.
Answer E
Answer: E
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After 2 year A removed his money; B and C continued the business for two more year. If the net profit after 3 years be Rs.4000, then A's share in the profit is?
Options:
A)460
B)289
C)220
D)400
E)640
Rationale: 2*24 : 3*36 : 4*36
4: 9: 12
4/25 * 4000 = 640
Answer: E
Answer: E
Question: What is the probability of rolling a total of 8 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side?
Options:
A)1/12
B)1/6
C)2/7
D)5/36
E)1/2
Rationale: Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 8 i.e. (2+6), (3+5), (4+4), (5+3), (6+2)
So, total probability is 5/36.
Answer is D.
Answer: D
Question: What is the smallest positive integer K such that the product of 2205 x K is a perfect square?
Options:
A)5
B)9
C)15
D)25
E)63
Rationale: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.
Now, 2205 = 3^2 * 7^7 * 5, so if k=5 then 2205 k = (3 * 7 * 5)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).
Answer: A.
Answer: A
Question: Which of the following will divide evenly into 347,456,520?
Options:
A)3
B)9
C)11
D)13
E)none of these
Rationale: Rule:
3: Sum of the digits should be divisible by 3
Given number : 3+4+7+4+5+6+5+2+0 =36 which is divisible by 3
Answer: A
Answer: A
Question: a, b, c, d, and e are positive consecutive odd integers and a < b < c < d < e.
If the sum of a+c+e is four less than the square of b, what is the product of de?
Options:
A)25
B)35
C)53
D)99
E)143
Rationale: a+c+e = bb - 4
Because we know the numbers are consecutive odd integers, we can rewrite the list as versions of the first number:
b = a+2
c = a+4
d = a+6
e = a+8
Therefore we can rewrite the original problem: a+(a+4)+(a+8) = (a+2)(a+2) - 4
Simplify: 3a + 4 + 8 = (aa + 4a + 4) - 4
Simplify: 3a + 12 = aa + 4a
Swap (just switch the sides in their entirety): aa + 4a = 3a + 12
Separate the number from the variables: aa + 4a - 3a = 12
Simplify: aa + a = 12
So the square of a, plus another a, equals 12. We can try out a few numbers quickly:
1x1 = 1, +1 = not 12
5x5 = 25, +5 = not 12
3x3 = 9, +3 = there we go!
So a = 3, and the sequence of consecutive odd numbers is 3, 5, 7, 9, 11.
The answer is the product of the last two numbers: 9x11 = 99 (option D).
Answer: D
Question: The Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result.
Options:
A)66
B)55
C)44
D)77
E)88
Rationale: 6th result = (58*6+63*6-60*11)
=66
Answer is A.
Answer: A
Question: Andrew started saving at the beginning of the year and had saved $200 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
Options:
A)11%
B)25%
C)44%
D)56%
E)70%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 540
Saving in 2nd year + 200 = 540
Saving in 2nd year = 540 - 200 = 340
Change in Value = 340 - 200 =140
Original Value = 200
Percentage Increase = (140 / 200 ) * 100 = 70% ..... Answer E......
Answer: E
Question: Find the number of different ways in which 7^11 can be expressed as the product of three factors
Options:
A)13
B)14
C)15
D)16
E)17
Rationale: let 7^11=7^x*7^y*7^z
then possible triplets of (x,y,z)
(0,0,11)(0,1,10)(0,2,9)(0,3,8)(0,4,7)(0,5,6)
(1,1,9)(1,2,8)(1,3,7)(1,4,6)(1,5,5)
(2,2,7)(2,3,6)(2,4,5)
(3,3,5)(3,4,4)
so number of different ways=16
ANSWER:D
Answer: D
Question: 144 candies are distributed to children with the same number. What can’t be the range including the number of children?
Options:
A)1~10
B)10~20
C)20~30
D)50~60
E)70~80
Rationale: -> In 144=1*144=2*72=4*36=6*24=8*18=9*16, you can come up with 4 cases. One is distributing 77 candies to 2 children each. Another is distributing 2 candies to 77 children each. Also, you can distribute 22 candies to 7 children. The other is distributing 7 candies to 22 children. Amongst these cases, what is not included is D. 50~60. Therefore, the answer is D.
Answer: D
Question: For dinner, Sandy ate 200 grams of corn which was five times as much corn as she ate for lunch, and twice as much corn as she ate for breakfast. How much corn did Sandy eat in total?
Options:
A)300
B)320
C)340
D)360
E)380
Rationale: For breakfast, Sandy ate 200 / 2 = 100 grams.
For lunch, Sandy ate 200 / 5 = 40 grams.
For dinner, Sandy ate 200 grams.
The total is 100 + 40 + 200 = 340 grams.
The answer is C.
Answer: C