divelab/Sys2Bench huggingface dataset:
Question: The regular price per can of a certain brand of soda is $0.60. If the regular price per can is discounted 20 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases?
Options:
A)$16.32
B)$18.00
C)$21.60
D)$34.56
E)$28.80
Rationale: The discounted price of one can of soda is (0.8)($0.60), or $0.48
Therefore, the price of 72 cans of soda at the discounted price would be (72)($0.48) = 34.56
Answer: D.
Answer: D
Question: Look at this series: 2, 3, 4, 9, 8,... What number should come next?
Options:
A)128
B)64
C)16
D)32
E)27
Rationale: Explanation: The given series is obtained by increasing powers of 2 and 3.
2*1 = 2
3*1 = 3
2*2 = 4
3*3 = 9
2*2*2 = 8
3*3*3 = 27 and so on.
Answer: Option E
Answer: E
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x?
Options:
A)80
B)96
C)100
D)108
E)120
Rationale: y = 0.5*0.5*x = x/4
y%*x = 36
(y/100)*x = 36
(x/400)*x = 36
x^2 = 36*400
x = 120
The answer is E.
Answer: E
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.45, b = 2.95, and c = 3.74, what is y – x?
Options:
A)-0.1
B)0
C)0.05
D)0.2
E)0.3
Rationale: To find x, we first sum a, b, and c, then round to the tenths place. 5.45 + 2.95 + 3.74 = 12.14, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 2.9 + 3.7 = 12.0.
We are looking for y - x, which gives us 12.2 - 12.0 = 0.2, or answer choice D.
Answer: D
Question: A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.
Options:
A)Rs.4500
B)Rs.5200
C)Rs.1800
D)Rs.3000
E)Rs.5000
Rationale: A:B:C = 5:6:4
Let the total profit = 100 - 30 = 70
5/15 * 70 = 70/3
A share = 70/3 + 30 = 160/3
B + C share = 100 - 160/3 = 140/3
A-(B+C) = 160/3 - 140/3 = 20/3
20/3 ---- 200
100 ---- ? => 3000
ANSWER:D
Answer: D
Question: Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 100 km and the other at the rate of 120 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)4.85
B)7.85
C)4.51
D)5.85
E)6.15
Rationale: T = (111 + 165)/ (100 + 120) * 18/5
T = 4.51
ANSWER:C
Answer: C
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12 m
B)161.12 m
C)111.82 m
D)111.19 m
E)131.12 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900
= 8000/9
= 888.88 m.
B can give C
= 1000 - 888.88
= 111.12 m.
Answer:A
Answer: A
Question: complete the following series
2, 4, 6, 10, ..... , 26
Options:
A)16
B)20
C)12
D)14
E)18
Rationale: In the series we can get the next term by adding the previous 2 terms.
so to get the answer we have to add 6 + 10 = 16
so the answer is option A) 16.
Answer: A
Question: 106 x 106 - 94 x 94 = ?
Options:
A)2400
B)2000
C)1904
D)1906
E)None of them
Rationale: =(106)^2-(94)^2
=(106+94)(106-94)
=(200 x 12)
=2400
Answer is A
Answer: A
Question: What is the value of n if the sum of the consecutive odd integers from 1 to n equals 169?
Options:
A)47
B)25
C)37
D)33
E)29
Rationale: # of terms = (n-1/2)+1 {(last term - first term)/2+1|
Sum = (1+n)/2 * # of terms
= (n+1)^2/4= 169
n+1 = 13*2
n+1 = 26
n=25.
ANSWER:B
Answer: B
Question: Which of the following describes all values of x for which 4-x^2 ≥ 0 ?
Options:
A)x ≥ 1
B)x ≤ -1
C)0 ≤ x ≤ 1
D)x ≤ -1 or x ≥ 1
E)-2 ≤ x ≤ 2
Rationale: 4-x^2 >= 0 ---> x^2-4<=0
--> (x+2)(x-2)<=0
Above equation true for
i) x+2<=0 and x-2>=0 ---> x<= -2 and x>=2 ---> this is not possible ---Strike out this solution
ii) x+2>=0 and x-2<=0 ---> x>=-2 and x<=2 --> -2<=x<=2
Answer E
Answer: E
Question: If x is an integer and y = 3x + 4, which of the following CANNOT be a divisor of y?
Options:
A)4
B)6
C)5
D)7
E)8
Rationale: For any value of x, the expression 3x + 4 would never be divisible by 3,6,9...... onwards
So answer = 6 = B
Answer: B
Question: Find the least number of complete years in which a sum of money put out at 45% compound interest will be more than double of itself?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 2 years
Answer: A
Answer: A
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)276 m
B)287 m
C)245 m
D)276 m
E)237 m
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C
Answer: C
Question: If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 72?
Options:
A)24
B)36
C)12
D)18
E)16
Rationale: The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
72=2*3*3*2*2 is divisible by 12. therefore the greatest common divisor is 12
C
Answer: C
Question: If TIER is written as 7183 and BRAIN is written as 23415, how is RENT coded ?
Options:
A)3653
B)3657
C)3857
D)2790
E)2711
Rationale: Explanation:
Given :
Letter : T I E R B A N
Code : 7 1 8 3 2 4 5
Thus, the code for RENT is 3857.
ANSWER:C
Answer: C
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 52 percent were employees. What percent were stockholders, who were not employees?
Options:
A)52
B)48
C)54
D)55
E)56
Rationale: I came up with the same answer choice B, but my approach was slightly different!
52% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 52% = 48%.
Answer: B
Question: P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in --- days if all of them are working together.
Options:
A)2
B)3 3⁄7
C)4 ¼
D)5
E)5 ¼
Rationale: Explanation :
Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/6
Work done by R in 1 day = 1/12
Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24
=> Working together, they will complete the work in 24/7 days = 3 3⁄7 days
Answer : Option B
Answer: B
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)900
B)190
C)277
D)262
E)223
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer: B
Answer: B
Question: A train 290 m long passed a pole in 29 sec. How long will it take to pass a platform 650 m long?
Options:
A)94 sec
B)89 sec
C)54 sec
D)27 sec
E)22 sec
Rationale: Speed = 290/29 = 10 m/sec.
Required time = (290 + 650)/10
= 94 sec.
Answer: A
Answer: A
Question: Ms. Adams sold two properties, X and Y, for $30,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
Options:
A)Loss of $1,250
B)Loss of $2,500
C)Gain of $1,250
D)Gain of $2,500
E)Neither a net gain nor a net loss
Rationale: Total %Loss = (Common Gain% or Loss%/10)^2
Hence Here Loss% = (20/10)^2 = 4%
which means he recovered only 96% of his investment which amount to a total revenue = 30000 + 30000 = 60000
i.e. 96% of cost = 60000
therefore, 4% of cost (Loss) = $2500
Answer: Option B
Answer: B
Question: If 100,000 microns = 1 decimeter, and 10,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
Options:
A)1.0e-05
B)0.0001
C)0.001
D)10,000
E)100,000
Rationale: Given that 100,000 microns = 1 decimeter =10,000,000,000 angstroms
So, 1 micron = 10,000,000,000/100,000
=100,000
Answer : E
Answer: E
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 1.5 grams per cubic centimeter and mineral Y weighs 3 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
Options:
A)2,400,000
B)2,800,000
C)55,000
D)28,000
E)280
Rationale: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 1.5 gms
In 400,000 cm^3 , X = 1.5 * 400,000 = 600,000 grams
In 1 cm^3, Y is 3 gms
In 600,000 cm^3, Y = 3 * 600,000 = 1,800,000 gms
Total gms in 1 m^3 = 600,000 + 1,800,000 = 2,400,000
ANSWER:A
Answer: A
Question: I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?
Options:
A)200
B)600
C)300
D)800
E)1000
Rationale: Let x be the number I chose, then
x/5−154=6
x/5=160
x=800
correct answer D
Answer: D
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
Options:
A)6:7
B)6:9
C)6:5
D)6:1
E)6:2
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer:C
Answer: C
Question: Find the principal if at 9% per annum simple interest, after 3 years the interest amounts to Rs. 2336 less than the principal?
Options:
A)1200
B)3450
C)3200
D)3500
E)3300
Rationale: P - 2336 = (P*9*3)/100
P = 3200
Answer: C
Answer: C
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 2years ago?
Options:
A)152460
B)214560
C)160000
D)210000
E)200000
Rationale: population 2 years ago = 176400/(1 + 5/100)^2
= 176400* 20/21 * 20/21
=160000
Answer is C
Answer: C
Question: A basket contains 3 blue, 5 black and 3 red balls. If 3 balls are drawn at random what is the probability that all are black?
Options:
A)2/33
B)3/33
C)33/2
D)8/33
E)9/33
Rationale: I suppose case is without replacement.
Probability for first to be black = 5/11
Probability for second to be black =4/10
Probability for third to be black = 3/9
Hence
Probability for all to be black = 5/11×4/10×3/9
= 2/33
Answer is A
Answer: A
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)7 sec
B)6 sec
C)8 sec
D)4 sec
E)2 sec
Rationale: Speed of train relative to man = 60 + 6
= 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55
= 6 sec.
Answer:B
Answer: B
Question: X alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and Y undertook to do it for Rs. 720. With the help of Z they finished it in 5 days. How much is paid to Z?
Options:
A)Rs 100
B)Rs 110
C)Rs 120
D)Rs 130
E)Rs 140
Rationale: (X+Y+Z)'s one day work=1/5 and (X+Y)'s one day work=1/15+1/10..
Z's one day work=1/30. ratio of one day work=1/15:1/10:1/30=2:3:1
therefore z will be paid=1/6*720=Rs 120.
ANSWER:C
Answer: C
Question: Mary's income is 60% more Than Tim's income and Tim's income is 30% less than Juan's income.What % of Juan's income is Mary's income.
Options:
A)112%
B)B.100%
C)96%
D)80%
E)64%
Rationale: Even I got 96%
J = 100
T = 100*0.7 = 70
M = 70*1.6 = 112
If Mary's income is x percent of J
M = J*x/100
x = M*100/J = 112*100/100 = 112
Ans:A
Answer: A
Question: A boatman can row 3 km against the stream in 20 minutes and return in 15 minutes. Find the rate of current ?
Options:
A)7/2 kmph
B)8/2 kmph
C)5/2 kmph
D)1.5 kmph
E)2/2 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/15 = 12 km/hr
Rate of current = (12-9)/2 = 1.5 km/hr.
Answer: D
Answer: D
Question: A fair sided dice labeled 1 to 6 is tossed two times. What is the probability of the dice obtaining the same value?
Options:
A)1/36
B)6/36
C)1/2
D)7/216
E)11/216
Rationale: The total possible number of combination if the dice is thrown 2 times is 36.
There are 6 possible outcomes that the number shown on the dice is the same.
The number are: (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)
Answer: B
Answer: B
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 7000. What was Simran's share in the profit?
Options:
A)Rs. 6423
B)Rs. 3000
C)Rs. 2,500
D)Rs. 4,000
E)None of these
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 7000 * 3/7 = Rs. 3000
ANSWER:B
Answer: B
Question: A 5-digit number is formed by the digits 2,4,5,6,8 (each digit used exactly once) . What is the probability that the number formed is divisible by 4 ?
Options:
A)2/5
B)3/5
C)4/5
D)6/5
E)7/5
Rationale: a no. is divisible by 4 if last two digit is divisible by 4
so numbers ending with 24,28,48,52,56,64,68,84 are divisible by 4
last two places are fixed by 24,28,48,52,56,64,68,84
so remaining 3 places can be filled in 3! ways for each
total=8*3!=48=n(E)
n(S)=5C4=120
p=48/120=2/5
ANSWER:A
Answer: A
Question: Of 45 applicants for a job, 21 had at least 4 years' experience, 27 had degrees, and 5 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
Options:
A)6
B)8
C)4
D)3
E)2
Rationale: 45 - 5 = 40
40 - 21 - 27 = -8
Then 8 are in the intersection between 4 years experience and degree.
Answer : B
Answer: B
Question: A car rental company charges for mileage as follows: 6 dollars per mile for the first n miles and 7 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
Options:
A)7d-n
B)6*7d-n
C)11d-n
D)13d-n
E)15d-n
Rationale: Total Distance in miles = d
Millage Charge = 6n + (d-n) 7
6n --> For the first n Miles
(d-n)7--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 7 .
If we solve the equation , We will get 7d-n
Answer : A
Answer: A
Question: If Z is a positive integer, which of the following must be odd?
Options:
A)x+1
B)Z^2+Z
C)Z^2+Z+1
D)x^2−1
E)3x^2−3
Rationale: A. Z+1 = can be odd or even. Since O + O =E or E + O = O
B. Z^2 + Z = Z(Z+1). Since from the above derivation we already know the term Z+1 can be Odd or Even, directly substitute here. Z(ODD) = Even (When Z is Even) or Z(EVEN) = EVEN [When Z is ODD]
C. Here's the answer. Since we know the term Z^2 + Z can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: C
Question: (√97+√486)/√54=?
Options:
A)2√2
B)2√3
C)3√2
D)3√3
E)13/3
Rationale: (√96+√486)/√54=(4√6+9√6)/3√6=13√6/3√6=13/3
Hence, the correct answer is E.
Answer: E
Question: If x*y = xy + 2(x + y) for all integers x and y, then 2* (–3) =
Options:
A)–16
B)–11
C)–8
D)4
E)16
Rationale: 2*(-3) = 2*(-3) + 2 (2 + (-3) ) = -6 -2 = -8
Option (C)
Answer: C
Question: A thief is spotted by a policeman from a distance of 225 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?
Options:
A)350m
B)200m
C)400m
D)900m
E)None of them
Rationale: Relative speed of the policeman = (10-8) km/hr =2 km/hr.
Time taken by police man to cover
(225m/1000) x 1/2 hr = 9/80 hr.
In 9/80 hrs, the thief covers a distance of 8 x 9/80 km = 9/10 km = 900 m
Answer is D.
Answer: D
Question: If x#y is defined to equal x^2/y for all x and y, then (-1#3)#3 =
Options:
A)4/3
B)1/3
C)1/27
D)-1/12
E)-4/3
Rationale: (-1)^2 / 3 = 1/3
(1/3)^2 / 3 = 1/27
so C is my answer
Answer: C
Question: If the radius of a cylinder is doubled and so is the height, what is the new volume of the cylinder divided by the old one?
Options:
A)8.
B)2
C)6
D)4
E)10
Rationale: let the radius be r and the the height be h.
New radius = 2r and height = 2h.
Area (new) : Area(old) = pi∗(2r)^2∗2h/pi∗r^2∗h = 8:1.
Hence the answer is A.
Answer: A
Question: Three coworkers P , E , R meet for Dinner. P had 5 sandwiches, E had 3 and R had none. Both PE share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PE, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
Options:
A)a) 5$
B)b) 3 $
C)c) 7 $
D)d) 4 $
E)e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
E:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: C
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Options:
A)30%
B)40%
C)50percent
D)60%
E)70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: C
Question: Q:Robert purchased $3500 worth of US saving bonds. If bonds are sold in $50 or $100 denominations only, which of the following CANNOT be the number of US saving bonds that Robert purchased?
Options:
A)20
B)27
C)50
D)70
E)80
Rationale: I started off with looking at the answer choices... 20-27-50 are in a tight range, so my guess was to look and rule out the bigger numbers.
The total amount is $3500. So with 80 bonds, each $50 = $4000 , we already exceed the $3500 limit. Hence E is the answer.
Answer: E
Question: 24 men working 8 hours a day can finish a work in 10 days. Working at the rate of 10 hours a day, the number of men required to finish the same work in 6 days is
Options:
A)30
B)36
C)34
D)32
E)None of these
Rationale: m1 × d1 × t1 × w2 = m2 × d2 × t2 × w1
24 × 10 × 8 × 1 = m2 × 6 × 10 × 1
⇒ m2 = 24×10×8/6×10= 32 men
Answer D
Answer: D
Question: A polygon has 104 diagonals. How many sides does it have?
Self made
Options:
A) 12
B) 13
C) 14
D) 15
E) 16
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 104
n*(n - 3) = 208
Substitute n from the answer choices. n = 16
Answer: E
Answer: E
Question: 2525 * 9
Options:
A)22725
B)25675
C)22655
D)27575
E)None of these
Rationale: Explanation:
2525 * (10 - 1)
= 25250 - 2525
= 22725
Option A
Answer: A
Question: what will come after
1,3,9,31,129
Options:
A)451
B)551
C)651
D)751
E)851
Rationale: 1*1+2 = 3
3*2+3 = 9
9*3+4 = 31
31*4 + 5 = 129
In same logic next number will be-
129*5 + 6 = 651
ANSWER:C
Answer: C
Question: Two integers are in the ratio of 1 to 3. If 10 is added to the smaller number, the ratio becomes 2 to 1. Find the larger integer.
Options:
A)6
B)9
C)10
D)12
E)15
Rationale: One option is to set up the equations and solve:
If the ratio of two integers x and y is 1 to 3, then 3x=y, where x is the smaller integer.
If adding 10 to the smaller integer makes the ratio 2 to 1, then x+10=2y.
Substituting y=3x into the second equation yields x+10=6x.
So, x=2 (smaller integer) and, y=3x=6 (larger integer) so A is the correct answer.
Another option is to TEST the answer choices.
A) the larger number is 6
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 2
If 10 is added to the smaller number, the ratio becomes 2 to 1
If we add 10 to the smaller number (2), we get 12.
So, the new ratio is 12 to 6 which is the same as 2 to 1.
Therefore choice A is correct.
B) the larger number is 9
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 3
If 10 is added to the smaller number, the ratio becomes 2 to 1
If we add 10 to the smaller number (3), we get 13
So, the new ratio is 13 to 9.
No good. We want a resulting ratio of 2 to 1
ELIMINATE B
C) the larger number is 10
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 3.33 (which is not an integer)
Since both numbers are integers, the larger number cannot be 10.
ELIMINATE C
D) the larger number is 12
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 4
If 10 is added to the smaller number, the ratio becomes 2 to 1
If we add 10 to the smaller number (4), we get 14
So, the new ratio is 14 to 12 which is 7 to 6.
No good. We want a resulting ratio of 2 to 1
ELIMINATE D
E) the larger number is 15
Given: the two integers are in the ratio of 1 to 3
So, the smaller number must be 5
If 10 is added to the smaller number, the ratio becomes 2 to 1
If we add 10 to the smaller number (5), we get 15
So, the new ratio is 15 to 15. This is the same as the ratio of 1 to 1
ELIMINATE E
Therefore A is the only correct choice.
Answer: A
Question: 7^6n -1^ 6n When n is an integer > 0 is divisible by
Options:
A)112
B)127
C)134
D)154
E)156
Rationale: 127
B
Answer: B
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Options:
A)2:3
B)3:2
C)1:3
D)4:3
E)3:4
Rationale: 5% of A + 4% of B = 2/3 (6% of A + 8% of B)
5/100*A + 4/100*B = 2/3(6A/100 + 8B/100)
==> A/20 + B/25 = A/25 + 4B/75
==> (1/20 - 1/25)A = (4/75 - 1/25)B
==> A/100 = B/75
==> A/B = 100/75 = 4/3
Required ratio = 4 : 3
Answer D) 4:3
Answer: D
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 1,000?
Options:
A)13
B)10
C)9
D)7
E)6
Rationale: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^9 = 512 <1,000, then the greatest possible length of integer z is 9.
The answer is C.
Answer: C
Question: Mona and Sona go around a circular track of length 400 m on a bike at speeds of 18 kmph and 36 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)120
B)80
C)60
D)136
E)150
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of monA , length of the track / speed of sona}
= LCM { 400/ (18 * 5/18) , 400/ (36 * 5 /18) }
= LCM (80, 40) = 80 sec.
Answer: B
Answer: B
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of five rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after___ minutes?
Options:
A)11 min
B)12 min
C)10 min
D)15 min
E)16 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 5 - 1 = 4 rounds per hour.
Time taken to complete one round at this speed = 1/4 hr = 15 min.
D
Answer: D
Question: If -4 < x < 7 and -7 < y < 3, which of the following specifies all the possible values of xy?
Options:
A)-42 < xy < 21
B)-49 < xy < 24
C)-28 < xy < 18
D)-24 < xy < 21
E)-24 < xy < 24
Rationale: The least value of xy is a bit more than 7*(-7)=-49 and the largest value of xy is a bit less than (-4)*(-6)=24.
Therefore -49 < xy < 24.
Answer: B.
Answer: B
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
Options:
A)5460
B)3377
C)2776
D)2887
E)2667
Rationale: 5000 * 104/100 * 105/100 => 5460
Answer: C
Answer: C
Question: If n is a natural number, then (6n^2 + 6n) is always divisible by?
Options:
A)6 only
B)Both 6 and 12
C)12 only
D)6 or 12
E)None
Rationale: 6n^2 + 6n = 6n(n + 1)
n(n + 1) is always even when n is a natural number
Hence 6n^2 + 6n is always divisible by 6 and 12
B)
Answer: B