divelab/Sys2Bench huggingface dataset:
Question: Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.
Options:
A)1683
B)1753
C)1523
D)1433
E)None of them
Rationale: L.C.M. of 5,6,7,8 = 840.
Therefore, Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Therefore, Required number = (840 X 2 + 3)=1683
Answer is A.
Answer: A
Question: 26 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Options:
A)625
B)650
C)576
D)600
E)700
Rationale: we can go in any bus out of the 26 buses.
Hence He can go in 26 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 25 ways.
Total number of ways = 26 x 25 = 650
ANSWER:B
Answer: B
Question: A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.600 more. What was the Sum?
Options:
A)Rs.1200
B)Rs.1300
C)Rs.1400
D)Rs.1500
E)Rs.1600
Rationale: At 5% more rate, the increase in S.I for 10 years = Rs.600 (given)
So, at 5% more rate, the increase in SI for 1 year = 600/10 = Rs.60/-
i.e. Rs.60 is 5% of the invested sum
So, 1% of the invested sum = 60/5
Therefore, the invested sum = 60 × 100/5 = Rs.1200 Answer: A
Answer: A
Question: Positive integer x has p factors; 3x has 3 factors; Which of the following values can p take?
I. 1
II. 2
III. 3
Options:
A)II or III
B)I or III
C)I or II
D)only I
E)only II
Rationale: Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer E
Answer: E
Question: Jeff has 252 ounces of peanut butter in 16, 28. and 40 ounce jars. He has an equal number of each sized jar. How many jars of peanut butter does Jeff have?
Options:
A)9
B)8
C)7
D)10
E)11
Rationale: Let p equal the number of each sized jarThen 16p + 28p + 40p = 25284p = 252p = 3Therefore, the total number of jars of peanut butter Jeff has = 3p = 9Answer: A
Answer: A
Question: Bricks are sold in packages of eight or thirteen only. If Timmy, a builder, bought 144 bricks exactly, what could be the number of large packs Timmy bought?
Options:
A)12
B)5
C)6
D)8
E)7
Rationale: Let number of packs of eight = e
let number of packs of thirteen = t
8e + 13t = 144
Now , we need to test for values of t .
Since sum 144 is even and 8s will always be even , t can't be odd .
Now , we can test for values e = 12 , 8 and 6
8*5 + 13*8 = 40 + 104 = 144
Answer D
Answer: D
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Mettur. Mettur, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mettur over the total taxable land of the village is:
Options:
A)0.20833
B)1.23455
C)2.45466
D)5.54353
E)6.45343
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
A
Answer: A
Question: Two circular frames are kept one above the other. Frame X has a diameter of 16 cm and Frame Y has a diameter of 12 cm. What fraction of the surface of Frame X is not covered by Frame Y?
Options:
A)3/5
B)7/16
C)12/16
D)24/12
E)2/3
Rationale: The questions asks us to find the surface which is not covered by the Frame Y i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem
Area of the Frame Y=pi* r^2, where r=6
=>pi*36
Area of the Frame X=pi*64
Surface not covered by the Frame Y=pi*64-pi*36=Pi*28
fraction of Frame X's surface is not covered by a Frame Y= Pi*28/total area of the Frame X
=28/64=7/16
Answer is B
Answer: B
Question: The product of two numbers is 192 and the sum of these two numbers is 28. What is the smaller of these two numbers?
Options:
A)10
B)12
C)14
D)15
E)16
Rationale: Solution
Let the number be x and (28 - x)	= Then,
x (28 - x) = 192
‹=›x2 - 28x + 192 = 0.
‹=›(x - 16) (x - 12) = 0
‹=›x = 16 or x = 12.
Answer B
Answer: B
Question: My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?
Options:
A)70
B)69
C)82
D)89
E)72
Rationale: Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,
365g = 52s.
Since my grandson is 12g months old,
12g = m.
Since my grandson, my son and I together are 120 years,
g + s + m = 120.
The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.
m / 12 + 365 m / (52 x 12) + m = 120 or
52 m + 365 m + 624 m = 624 x 120 or
m = 624 x 120 / 1041 = 72.
Answer: E
Question: Find the unit digit in
(544)102+(544)103
Options:
A)2
B)4
C)0
D)1
E)3
Rationale: Explanation:
Required digit is =
(4)102+(4)103
as
(4)2
gives unit digit 6 so
(4)102
unit digit is 6 and
(4)103
unit digit is, unit digit of
6×4
= 4, so answer will be unit digit of 6 + 4 = 0
Option C
Answer: C
Question: A customer pays 50 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
Options:
A)50
B)40
C)70
D)60
E)20
Rationale: Let x be the original price.
x - 20 = 50
x - 20 + 20 = 50 + 20
x + 0 = 70
x = 70
Answer: C
Question: For any non-zero a and b that satisfy |ab| = ab and |a| = a
|b - 4| + |ab - b| = ?
Options:
A)ab-4
B)2b - ab - 4
C)ab+4
D)ab - 2b + 4
E)4-ab
Rationale: |ab| = ab and |a| = -a
=> b is also negative.
So
|b-4| + |ab -b|
= (b-4) + ab - b ( as ab is positive and -b is positive, so expression is totally positive)
=b-4+ab-b
=ab-4
Answer -A
Answer: A
Question: The value of x + x(xx) when x = 8
Options:
A)A) 520
B)B) 516
C)C) 518
D)D) 536
E)E) 564
Rationale: x + x(xx)
Put the value of x = 8 in the above expression we get,
8 + 8(88)
= 8 + 8(8 Ã— 8)
= 8 + 8(64)
= 9 + 512
= 520 The answer is (A)
Answer: A
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
Options:
A)9:1
B)4:2
C)5:2
D)9:2
E)9:0
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Answer:A
Answer: A
Question: Sally has to pick her son up at 2 p.m. It is now 12:30 p.m. She has to travel 53 miles to get her son from camp. What time should she leave to pick her on up with the closest time to 2 p.m, without being late, given the distance of 53 miles with a constant speed of 50 mph?
Options:
A)She needs to leave at 12:53 pm
B)She needs to leave at 12:57 p.m
C)She needs to leave at 1:03 p.m
D)She cannot get there in time.
E)She needs to leave at 1:15 p.m
Rationale: B, she is traveling 50 miles per hour and needs to travel 53 miles. Given that 50/53= 1.03 so approximately 1 hour and 3 minutes. 2 p.m- 1 hour 3 minutes= 12:57 pm. While A gets her there on time it is not as close to 2pm.
Answer: A
Question: If A and B are digits and 5AB is a 3-digit number that is divisible by 10, which of the following is a possible product of A and C?
Options:
A)57
B)21
C)52
D)38
E)50
Rationale: Key to this question is to remember the fact that a number divisible by 10 must end with only 0 (i.e B).
If B had to be 0, product should also be 0 regardless of A.
Only one answer choice meets the requirement.
Ans E.
Answer: E
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?
Options:
A)65 minutes
B)76 minutes
C)70 minutes
D)62 minutes
E)52 minutes
Rationale: 1/20 - 1/28
= 1/70
70 minutes
Answer:C
Answer: C
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 27 less than n. What is y in terms of x ?
Options:
A) 10 - x
B) 9 - x
C) x + 3
D) x - 3
E) x - 9
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 27 less than 10x+y
10x+y-27=10y+x
10x-x-27=10y-y
9x-27=9y
x-3=y
OR
y=x-3
Ans:D
Answer: D
Question: A polling company surveyed a certain country, and it found that 35% of that country’s registered voters had an unfavorable impression of both of that state’s major political parties and that 20% had a favorable impression only of Party Q. If one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of Party B, then what percentage of the country’s registered voters have a favorable impression of both parties (assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only)?
Options:
A)15
B)20
C)30
D)35
E)45
Rationale: S=100
not( Q and B ) =35
only Q=20
(Q and B)/B=1/2
let ( Q and B ) =x
only B =2x
so now, 20+35+x+2x=100
x= 15
A ans
Answer: A
Question: 2 + 2^2 + 2^3 + ... + 2^8 = ?
Options:
A)510
B)310
C)210
D)410
E)None of them
Rationale: Given series is a G.P. with a = 2, r = 2 and n = 8.
sum = a(r^n-1)/(r-1) = 2 x (2^8 –1)/(2-1)= (2 x 255) =510
Answer is A.
Answer: A
Question: A textile manufacturing firm employees 50 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 50 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
Options:
A)13000
B)7000
C)10000
D)5000
E)None of these
Rationale: Explanation :
Profit = 5,00,000−(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000×(49/50)−150000×(49/50)−75000.
=>Rs 2,68,000.
Decrease in profit
=>2,75,000−2,68,000
=>Rs. 7,000.
Answer : B
Answer: B
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 70 as remainder. Find the no. is?
Options:
A)145646
B)236578
C)645353
D)456546
E)220070
Rationale: (555 + 445) * 2 * 110 + 70 = 220000 + 70 = 220070
E
Answer: E
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 151?
Options:
A)2050
B)2350
C)2650
D)2950
E)3250
Rationale: 100 + 102 + ... + 150 =
100*26 + (2+4+...+50) =
100*26 + 2*(1+2+...+25) =
100*26 + 2(25)(26)/2 =
100*26 + 25*26 = 125(26) = 3250
The answer is E.
Answer: E
Question: A can do a job in 10 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)14 days
B)15 days
C)22 days
D)11 days
E)19 days
Rationale: B
1/10 + 1/30 = 2/15
15/2 *2 = 15 days
Answer: B
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
Options:
A)12 kg
B)60 kg
C)72 kg
D)96 kg
E)None of these
Rationale: Explanation:
Volume of water displaced = (3 x 2 x 0.01) m3
= 0.06 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.06 x 1000)kg
= 60 kg.
Answer: B
Answer: B
Question: if p/q=3/4
then3p+8q=?
Options:
A)25/4
B)25/2
C)20/4
D)41/4
E)25/3
Rationale: 3p+8q=?
Divided by q,
3(p/q)+8=x
3*(3/4)+8=41/4
ANSWER:D
Answer: D
Question: A man took loan from a bank at the rate of 10% p.a. simple interest. After 3 years he had to pay Rs. 3000 interest only for the period. The principal amount borrowed by him was:
Options:
A)8000
B)10000
C)11000
D)12000
E)13000
Rationale: Principal = (100X3000)/(10X3)= Rs. 10000
answer : B
Answer: B
Question: The ratio between the speeds of two trains is 8: 9. If the second train runs 270 kms in 3 hours, then the speed of the first train is ?
Options:
A)85 km/hr
B)835 km/hr
C)80 km/hr
D)82 km/hr
E)None of these
Rationale: Explanation:
Let the speeds of two trains be 8X and 9X km/hr.
9/X=270/3=>X=10Km/hr
So speed of first train is 10*8 = 80 km/hr
Option C
Answer: C
Question: An unbiased cubic die is thrown.What is the probability of getting a multiple of 2 or3?
Options:
A)1/2
B)1
C)1/6
D)4/6
E)5/6
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
Let F be the event of getting the multiple of 2
then ,E={2,4,6}
Let G be the event of getting the multiple of 2 and 3
then ,G={2,3,4,6}
P(G)=n(G)/n(S)=4/6
ans D
Answer: D
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 174 votes. Find the total number of valid votes?
Options:
A)435
B)570
C)480
D)520
E)550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 174 => 4x/10 = 174
=> 4x = 1740 => x = 435.
ANSWER:A
Answer: A
Question: Mrs. A. invested $21,000; part at 5%, and part at 8%. The total interest on the investment was $1,470. How much did she invest at each rate?
Options:
A)x=$15,000, y =$30,000
B)x=$12,000, y =$24,000
C)x=$8,000, y =$16,000
D)x=$10,000, y =$20,000
E)x=$7,000, y =$14,000
Rationale: I approached this question like a mixture problem.
I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.
Anyway here's how I did it.
0.05(x) + 0.08(y) = 0.07(x+y)
0.01(y) = 0.02(x)
y = 2x
Note: 0.07(x+y) because $1,470 is 7% of 21,000
In which answer choice is y = 2(x)
Answer E
Answer: E
Question: In a class, 30 students pass in English and 20 students in Math, while some students among these pass in both. How many more students do only English as compared to those doing only Maths?
Options:
A)10
B)15
C)20
D)25
E)Indeterminate
Rationale: Let us consider tht x student are tohse who passed in both English and Maths...
So first we remove x student from both of them
Therefore,
English = 30-x
Maths = 20-x
Now, Number of Students more in English = (30-x)-(20-x)
= 30-x-20+x
= 10
ANSWER:A
Answer: A
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?
Options:
A)230 m
B)270m
C)643m
D)832m
E)270m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 250/26	= 20
x + 250 = 520
x = 270.
Answer:B
Answer: B
Question: The errand service company gets a discount at the fuel center when they fill up more than 4 cars at a time. The service is $1.10 per vehicle and .30 cents per liter of fuel. On Monday , they will fill 3 vans and 3 cars. The cars are 25 liters each and the vans are 60% bigger. How much will it cost to fill up all vehicles if they are empty?
Options:
A)$65.50
B)$68.10
C)$67.50
D)$68.50
E)$65.10
Rationale: Lots of calculations.
1.10*6 + 3*25*.30+ 25*(8/5)*3*.30
Answer=$65.10
The correct option is E.
Answer: E
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
Options:
A)Friday
B)Saturday
C)Sunday
D)Wednesday
E)WednSDA
Rationale: n 31st December, 2005 it was Saturday.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
Answer: A
Answer: A
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options:
A)12:15:17
B)12:15:16
C)12:15:10
D)12:15:155
E)12:15:11
Rationale: Aman : Rakhi : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12:15:16
Answer: B
Answer: B
Question: Complete the series 95, 115.5, 138, ..., 189
Options:
A)189
B)198
C)178
D)187
E)193
Rationale: 95 + 20.5 = 115.5
115.5 + 22.5 = 138
138 + 24.5 = 162.5
162.5 + 26.5 = 189
Answer is A.
Answer: A
Question: Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.3 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
Options:
A)$1.75
B)$1.85
C)$2.00
D)$2.12
E)$2.30
Rationale: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.
We're told that there are 6 pots and that each pot costs 30 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.
Since the total price is $8.25 (a 30-cent increment) and the the difference in sequential prices of the pots is 30 cents, the largest pot PROBABLY has a price that is a 30-cent increment. From the answer choices, I would then TEST Answer D
IF....
The largest pot = $2.125
The other 5 pots are....
0.625
0.925
1.225
1.525
1.825
2.125
Total = $8.25
So this MUST be the answer.
D
Answer: D
Question: Evaluate the sum
1-2 +3-4 + 5-6 +... + 997-998 + 999-1000
Options:
A)-500
B)-1000
C)-999
D)-1001
E)500500
Rationale: One groups the first two terms and each successive two terms to obtain a sum of
500 expressions each of which is -1. The answer is -500
correct answer A
Answer: A
Question: A train passes a man standing on the platform. If the train is 180 meters long and its speed is 72 kmph, how much time it took in doing so?
Options:
A)6 Â½ sec
B)6 Â½ sec
C)9 Â½ sec
D)9 sec
E)7 Â½ sec
Rationale: D
9 sec
D = 180
S = 72 * 5/18 = 20 mps
T = 180/20 = 9 sec
Answer: D
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, 17, 22, 20, (....)
Options:
A)27
B)20
C)22
D)24
E)26
Rationale: There are two series (8, 11, 14, 17, 20) and (7, 12, 17, 22, 27) increasing by 3 and 5 respectively.
answer : A
Answer: A
Question: A person travels from K to L a speed of 50 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips ?
Options:
A)50 kmph
B)70 kmph
C)60 kmph
D)80 kmph
E)10 kmph
Rationale: Explanation:
Speed on return trip = 150% of 50 = 75 km/hr.
Average speed = (2 x 50 x 75)/(50 + 75) = 60 km/hr.
Answer: C
Answer: C
Question: A pair of articles was bought for $1000 at a discount of 10%. What must be the marked price of each of the article?
Options:
A)$555.55
B)$500
C)$350
D)$400
E)$600
Rationale: S.P. of each of the article = 1000/2 = $500
Let M.P = $x
90% of x = 500
x = 500*100/90 =$555.55
Answer is A
Answer: A
Question: In a hotel we can order two types of varities,but we can make 6 more variteis in home.One can choosethe four varities with two from hotel as must.Find how many ways one can order.
Options:
A)14
B)15
C)56
D)28
E)30
Rationale: No. of ways=2c2*6c2=15
ANSWER:B
Answer: B
Question: If 2/z = 2/(z + 1) + 2/(z + 25) which of these integers could be the value of z?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: Solving for z algebraically in this problem would not be easy. Instead, we can follow the hint in the question (“which of these integers…”) and test each answer choice:
A. 2/0 = 2/1 +2/25 INCORRECT (Division by zero)
B. 2/1 = 2/2 +2/26 INCORRECT
C. 2/2 = 2/3 +2/27 INCORRECT
D. 2/3 = 2/4 +2/28 INCORRECT
E. 2/4 = 2/5 +2/30 CORRECT
The correct answer is E, because it contains the only value that makes the equation work. Notice how quickly this strategy worked in this case
Answer: E
Question: A and B together do a work in 20 days.B and C together in 15 days and C and A in 12 days.so A,B and C together finish same work in how many days?
Options:
A)12
B)15
C)8
D)10
E)11
Rationale: (A+B) work in 1 day= 1/20,(B+C) work in 1 days = 1/15.,(C+A) work in 1 days=1/12
(1) adding=2[A+B+C] in 1 day work = [1/20+1/15+1/12]=1/5
(A+B+C) work in 1 day= 1/10
So,all three together finish work in 10 days
Answer D
Answer: D
Question: If x is 40 percent greater than 88, then x =
Options:
A)68
B)70.4
C)123.2
D)105.6
E)108
Rationale: x=88*1.4=123.2
So the answer is C.
Answer: C
Question: Of the mutual funds on a “select list,” 2/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 100 funds on the list have 3-star ratings, how many funds are on the list?
Options:
A)500
B)750
C)1,000
D)1,200
E)1,500
Rationale: A
Fraction of 5- and 4-star funds: 2/3 + (2/5)*(1/3) = 2/3 + 2/15 = 12/15=4/5
Fraction of 3-star funds = 1 - 4/5 = 1/5
(1/5)*Total = 100
Total = 500
Answer: A
Question: How many positive integers will divide evenly into 440?
Options:
A)8
B)12
C)16
D)18
E)20
Rationale: 520 = 10*13*4 = 8*5*13 = 2^3*5*13
We need to positive integers will divide evenly into 520 or simply the factors of 520
If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)
Therefore, number of factors of 520 = (3+1)*(1+1)*(1+1) = 4*2*2 = 18
Option D
Answer: D
Question: The bankerâ€™s discount of a certain sum of money is Rs. 80 and the true discount on the same sum for the same time is Rs. 70. The sum due is
Options:
A)210
B)280
C)560
D)450
E)None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[80 * 70 / 80 - 70] = Rs. [80 * 70 / 10] = Rs. 560
Answer C
Answer: C
Question: Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $50 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge for the calls he made in January, what is Elvin's fixed monthly charge for Internet service?
Options:
A)$5
B)$10
C)$14
D)$24
E)$28
Rationale: Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $50
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 50
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 50
i.e. x = 26
i.e. Fixed Monthly Charge, y = 26
Answer: D
Answer: D
Question: The average of 45 students in a class is 18 years. The average age of 21 students is 16. What is the average age of remaining 14 students?
Options:
A)21
B)16
C)17
D)18
E)19
Rationale: Sum of the ages of 14 students
= (18* 45) - (18 * 21) = 810 - 378 = 432
Required average = (266/23)
= 18 years.
Answer: D
Answer: D
Question: If 2x +3y = 30 and (x+y)/y = 11/8, then find the value of 5y + 6x
Options:
A)72
B)58
C)64
D)29
E)28
Rationale: Explanation:
The given equations are :
2x + 3y = 30 --------- (i)
and, (x+y)/y = 11/8
8x + 8y = 11y
8x – 3y =0 ----(ii)
Adding (i) & (ii), we get : 10 x = 30 or x = 3.
Put x = 3 in (i), we get : y = 8
Therefore, 5y + 6x = (5 * 8 + 6 * 3) = 40 + 18 = 58.
ANSWER: B
Answer: B
Question: If 0 < c < 1, what is the median of the values c, c^-1, c^2, c^1/2 and c^3?
Options:
A)c
B)c^-1
C)c^2
D)c^1/2
E)c^3
Rationale: A. To make the problem less confusing, I picked a number between 0 and 1 such as c = 1/4 and calculate:
c = 1/4
c^-1 = 4
c^2 = 1/16
c^(1/2) = 1/2
c^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is c. Answer A
Answer: A