divelab/Sys2Bench huggingface dataset:
Question: The area of a rectangular field is equal to 800 square meters. Its perimeter is equal to 120 meters. Find the width of this rectangle.
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: L * W = 800 : area , L is the length and W is the width.
2 L + 2 W = 120 : perimeter
L = 60 - w : solve for L
(60 - W) * W = 800 : substitute in the area equation
W = 20 and L = 40
correct answer D
Answer: D
Question: If the cost price of 50 articles is equal to the selling price of 32 articles, then the gain or loss percent is?
Options:
A)22
B)56.25
C)78
D)33
E)25
Rationale: Given that, cost price of 50 article is equal to selling price of 32 articles.
Let cost price of one article = Rs. 1
Selling price of 32 articles = Rs. 50
But Cost price of 32 articles = Rs. 32
Therefore, the trader made profit.\Percentage of profit = 18/32 * 100 = 56.25%
Answer:B
Answer: B
Question: Alice the number theorist knows the rule for testing if a number n is divisible by 3:
n is divisible by 3 if and only if the sum of the digits of n is divisible by 3.
When Alice visits Mars, she finds that the Martians have six hands, and six fingers on each
hand, so that they count in base 36. In base 36, Alice’s divisibility test doesn’t work for testing
divisibility by d = 3. But it does work for one of the d listed below. Which one?
Options:
A)4
B)7
C)10
D)11
E)15
Rationale: First of all, why does the rule work in base 10 for 3? It works because 10-1 = 3*3,
100 -1 = 3 *33, 1000 - 1 = 3 * 333, etc. As a result, the expressions
a0 + a1 *10 + a2 /102 + a3 /103 + ... + ak *10k
and
a0 + a1 + a2 + a3 + ...+ ak
differ by a multiple of 3.
The key point is that 3 |(10 - 1). It is quite easy to see that this is a necessary condition. We
can see that it is sufficient because 100-1 = (10-1) *(10+1), 1000-1 = (10*1)(100+
10 + 1), etc. So, in base 36, we must have d | (36 - 1). Therefore, d must be a divisor of 35,
and the only such divisor listed is 7.
correct answer B
Answer: B
Question: The perimeter of a square is 64 m. Find the area of the square.
Options:
A)161 mÂ².
B)164 mÂ².
C)166 mÂ².
D)256 mÂ².
E)273 mÂ².
Rationale: Perimeter of square = 64 m
But perimeter of square = 4 Ã— side
Therefore, 4 Ã— side = 64 m
Therefore, side= 64/4 m = 16m
Now, the area of the square = (side Ã— side)
Therefore, area of the square = 16 Ã— 16 mÂ² = 256 mÂ².
ANSWER : OPTION D
Answer: D
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.672 find the share of A.
Options:
A)256
B)388
C)379
D)277
E)122
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 672 = 256
Answer: A
Answer: A
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.60 only. Menâ€™s wages are?
Options:
A)6Rs
B)2Rs
C)4Rs
D)9Rs
E)3Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 60 Rs.
5M + 5M + 5M ----- 60 Rs.
15M ------ 60 Rs. => 1M = 4Rs.
Answer: C
Answer: C
Question: Look at this series: 72, 76, 73, 77, 74, __, 75, ... What number should fill the blank?
Options:
A)44
B)78
C)15
D)92
E)29
Rationale: D
78
This series alternates the addition of 4 with the subtraction of 3.
Answer: D
Question: The number which exceeds 16% of it by 63 is :
Options:
A)75
B)52
C)58
D)60
E)62
Rationale: Solution
Solution
Let the number be x.
x-16% of x =63
x-16/100x =63
x-4/25x=63
21/25x=63
x=(63x25/21)= 75
Answer A
Answer: A
Question: The sector of a circle has radius of 21 cm and central angle 108o. Find its perimeter?
Options:
A)81.6cm
B)85.9cm
C)90cm
D)92cm
E)95cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (108/360 * 2 * 22/7 * 21) + 2(21)
= 39.6 + 42 = 81.6 cm
Answer:A
Answer: A
Question: 6 3/4 + 7 2/17 - 9 1/15=?
Options:
A)7 719/1020
B)9 817/1020
C)9 719/1020
D)4 817/1020
E)None of them
Rationale: Given sum=6+3/4+7+2/17-(9+1/15)
=(6+7-9)+(3/4+2/17-1/15)
=4+(765+120-68/1020
=4 817/1020
Answer is D
Answer: D
Question: One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle?
Options:
A)2sqrt(61)
B)2sqrt(62)
C)2sqrt(63)
D)2sqrt(64)
E)2sqrt(65)
Rationale: base of triangle is 20 and area is 80
therefore height=2*80/20=8.
now one side of triangle is of 10.
so we can get the point were the base is divided by applying Pythagoras therm
so division pt =sqrt(10^2-8^2)=sqrt(36)=6
threfore other half is 14.
now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65)
ANSWER:E
Answer: E
Question: Tomy's age 24 years hence will be thrice his age four years ago. Find Tomy's present age?
Options:
A)12 years
B)13 years
C)15 years
D)17 years
E)18 years
Rationale: Let MTomy's present age be 'x' years.
x+ 24 = 3(x- 4)
=> 2x = 36 => x = 18 years.
E
Answer: E
Question: A trader has 50 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
Options:
A)5 and 45 kg
B)10 and 40 kg
C)15 and 35 kg
D)20 and 30 kg
E)40 and 30 kg
Rationale: Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 50/1+9 *1 = 5 kg
Quantity sold at 6% loss = 50/1+9 *9 = 45kg
ANSWER:A
Answer: A
Question: In a mixed college 160 students are there in one class. Out of this 160 students 3/8 students are girls. How many boys are there ?
Options:
A)A)40
B)B)60
C)C)80
D)D)100
E)E)140
Rationale: Total Number of Students :160
Total Girls : 160*3/8 =60
Total Boys : 160-60 = 100
Answer is D
Answer: D
Question: A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit?
Options:
A)75.65
B)73.26
C)72.5
D)70.78
E)71.62
Rationale: Explanation:
We are given selling price = Rs. 580 and expected profit of 15 %
Therefore, we can easily solve this numerical, considering basic formulae of profit and loss.
Let cost price = x
Selling price = C.P. + Profit
S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price)
580 = x + (0.15 x)
580 = 1.15 x
Therefore,
x = 504.347
Cost Price = Rs. 504.35
Now, we have the cost price and hence,
Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65
The trader gets a profit of Rs. 75.65
ANSWER IS A
Answer: A
Question: Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?
Options:
A)10 years
B)38 years
C)39 years
D)64 years
E)67 years
Rationale: current age = 26 years because Nitin's age was equal to square of some number ( 25= 5^2) last year and the following year it would be cube of a number (27= 3^3).
Next cube age will be 64 =4^3 which will come after 64-26 = 38 years.
ANSWER:B
Answer: B
Question: Share Rs.6000 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
Options:
A)900
B)980
C)1200
D)1240
E)2000
Rationale: Amount received by sanjay.
4 / 12 X 6000 = 2000= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 2000.
E
Answer: E
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. 24,500. What was Simran's share in the profit?
Options:
A)2777
B)2999
C)2799
D)2781
E)10500
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E
Answer: E
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.899] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
Options:
A)0
B)1
C)27
D)54
E)0
Rationale: K=[lCM of 80 and 45] * (any integer)
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
for value of k(60) * any integer unit value will be always zero .
E
Answer: E
Question: A freight elevator can carry a maximum load of 1140 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
Options:
A)45
B)85
C)190
D)215
E)210
Rationale: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1140 - 200 - 430 = 510.
allowed per package = 510 / 3 = 170
So difference in average of existing and allowable = 215 - 170 = 45
Hence A
Answer: A
Question: The product of a and b is equal to 14 more than twice the sum of a and b. If b = 8, what is the value of b - a?
Options:
A)2
B)3
C)7
D)24
E)35
Rationale: ab= 14 + 2(a+b)
8a= 14+2a +16
6a= 30
a=5
b-a= 8-5=3
B is the answer
Answer: B
Question: A batsman makes a score of 76 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
Options:
A)36
B)28
C)42
D)45
E)None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 76 = 17x or x = (76 – 48) = 28.
Answer B
Answer: B
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
Options:
A)11 1/8%
B)11 1/5%
C)11 1/9%
D)11 7/9%
E)21 1/9%
Rationale: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer: C
Answer: C
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
Options:
A)3:6:7
B)3:4:7
C)9:4:7
D)3:4:6
E)3:5:7
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
Answer: B
Answer: B
Question: Suresh Raina and Gautam Gambhir after a scintillating IPL match decide to travel by cycle to their respective villages. Both of them start their journey travelling in opposite directions. Each of their speeds is 6 miles per hour. When they are at a distance of 50 miles, a housefly starts flying from Suresh Raina's cycle towards Gautam Gambhir at a relative speed of 17 miles per hour with respect to Raina's speed. What will be the time taken by housefly to reach Gambhir?
Options:
A)37
B)10
C)27
D)36
E)19
Rationale: Fly speed is 17 kmph w.r.t to suresh as fly is moving in opposite direction to suresh, its actual speed is 17 - 6 = 11.
Now relative speed of fly and gambhir = 11 - 6 = 5 kmph
So fly takes = 5011−65011−6 = 10 Hrs
Answer:B
Answer: B
Question: If 5+3+2=151022, 9+2+4=183652, then 7+2+5=?
Options:
A)223888
B)143547
C)2607778
D)126997
E)127811
Rationale: If the given number is a + b + c then a.b | a.c | a.b + a.c - b
⇒⇒ 5+3+2 = 5.3 | 5.2| 5.3 + 5.2 - 3 = 151022
⇒⇒ 9+2+4 = 9.2 | 9.4 | 9.2 + 9.4 - 2 = 183652
7+2+5= 7.2 | 7.5 | 7.2 + 7.5 - 2 = 143547
Answer:B
Answer: B
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 15 hour to row to a place and come back, how far is the place?
Options:
A)24km
B)30km
C)48km
D)72km
E)15km
Rationale: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 15
2x+3x = 360
x = 72 km
Answer is D
Answer: D
Question: Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet?
Options:
A)120 km
B)360 km
C)480 km
D)500 km
E)None
Rationale: Sol.
Suppose they meet x hours after 14.30 hrs.
Then, 60x = 80 (x - 2) or x = 8.
∴ Required distance = (60x8)km = 480 km.
Answer C
Answer: C
Question: If x/y = 3/z, then 9z^2 =
Options:
A)y²/ x²
B)x²y²
C)81y²/ x².
D)9y/x
E)x²/y²
Rationale: This question is most easily solved by isolating y in the equation and substituting into the expression 9z²:
x/y = 3/z
x = 3y/z
3y = xz
z = 3y/x.
If we substitute 3y/xinto the expression for z, we get:
9(3y/x)² = 9(9y²/ x²) = 81y²/ x².
The correct answer is choice (C)
Answer: C
Question: A train running at the speed of 100 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)298 m
B)250 m
C)208 m
D)988 m
E)299 m
Rationale: Speed = 100 * 5/18 = 250/9 m/sec
Length of the train = speed * time = 250/9 * 9
= 250 m
Answer:B
Answer: B
Question: 30% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
Options:
A)70
B)97
C)87
D)100
E)76
Rationale: Given, 30% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 30% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/30 = 80
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (80 + 120)/2 = 100.
Answer:D
Answer: D
Question: Each of the following numbers has a remainder of 3 when divided by 8 except:
Options:
A)11
B)19
C)3
D)83
E)26
Rationale: It's E
26 = 8*3+2
Answer: E
Question: Sharmeeka is putting all of her pens in order by number. One has the number 4 on it, the next has number 8, the next has number 12, and the next has number 16.
What number will the next pen have on it?
Options:
A)20
B)25
C)32
D)22
E)24
Rationale: A) 20, because the pens are ordered by multiples of 4.
4 +4 = 8
8 + 4=12
12+4=16
16+4=20
Answer: A
Question: A standard Veggiematik machine can chop 20 carrots in 2 minutes. How many carrots can 3 standard Veggiematik machines chop in 3 minutes?
Options:
A)81
B)90
C)121
D)130
E)144
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 20 Carrots - 2 minutes,
1 standard Veggiematik machine - 10 Carrots - 1 minute,
Now
3 standard Veggiematik machine - ? Carrots - 3 minutes,
Hence = 10X3X3 =90 Carrots
Answer B
Answer: B
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 40% profit on the cost of the item?
Options:
A)18
B)30
C)22
D)22.5
E)27
Rationale: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 40% of the final price --> (final price)*0.6 = $18 --> (final price) = $30.
Answer: B.
Answer: B
Question: The sector of a circle has radius of 14 cm and central angle 135o. Find its perimeter?
Options:
A)91.5 cm
B)61 cm
C)28.9 cm
D)29.2 cm
E)98.2 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 14) + 2(14)
= 33 + 28 = 61 cm
Answer:B
Answer: B
Question: If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of Rs. 1000
Options:
A)10
B)20
C)30
D)40
E)60
Rationale: Explanation:
Clue: Answer will be 5% of 1000 - 4% of 1000
Option A
Answer: A
Question: The simple interest on a sum of money is 5/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
Options:
A)5 4/9%
B)17 4/9%
C)7 4/9%
D)8 4/9%
E)9 4/9%
Rationale: 5/9 P = (P*R*R)/100
R = 22.36/3 = 7 4/9%
ANSWER:C
Answer: C
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
Options:
A)3500
B)3900
C)3750
D)3840
E)3950
Rationale: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y =	(5/2)x.
15x + 2y = 4000
15x + 2 x	(5/2)	x = 4000
20x = 4000
x = 200.
So, y =(5/2)x 200= 500.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
Answer is B.
Answer: B
Question: The greatest number by which the product of three consecutive multiples of 4 is always divisible is
Options:
A)54
B)76
C)152
D)384
E)None of these
Rationale: Solution
Required number	= Product of first three multiplies of 3
= (4 Ã— 8 Ã— 12)= 384.
Answer D
Answer: D
Question: A man whose speed is 7.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)10
B)8
C)9
D)7.2
E)6
Rationale: M = 7.5
S = 1.5
DS = 9
US = 6
AS = (2 * 9 * 6) /15 = 7.2
Answer: D
Answer: D
Question: What is the smallest integer n that satisfies both of the following equations, in which p and q
are positive integers?
n = p2 + p
n = q2 + q + 2014
Options:
A)2024
B)2034
C)2056
D)2070
E)2196
Rationale: The term 2014 in the second equation suggests trying small numbers for q, and a
little experimentation with p close to the square root of 2014 and n = p(p + 1) leads fairly
quickly to q = 7, giving n = 2070, which is (45)(46)
correct answer D
Answer: D
Question: What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9.
I. The number is multiple of 51.
II. The sum of the digits a and b is 6.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: From statement I:
A two digit number, greater than 9 and multiple of 51 should be 51 itself.
Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer.
From statement II:
A two digit number, greater than 9 and sum of the digit is 6.
It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone.
Thus, I alone give the answer while II alone not sufficient to answer.
ANSWER A I alone sufficient while II alone not sufficient to answer
Answer: A
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
Options:
A)187 cm2
B)178 cm2
C)285 cm2
D)178 cm22
E)287 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
285 cm2
Answer: C
Answer: C
Question: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Options:
A)14 min 19 sec
B)14 min 42 sec
C)14 min 20 sec
D)14 min 40 sec
E)14 min 10 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.Answer: D
Answer: D
Question: Jerry and Jim are opposing participants in an online auction. Each has a constant bidding strategy: Jerry always bids up by raising $40 over any previous bid. Jim always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: Jerry bids up first, and Jim follows. Jerry bids up again, and Jim follows and raises the bid to a final $600. What was the dollar value of the initial price?
Options:
A)90
B)465
C)656
D)345
E)35
Rationale: Initial bid = p$
Jerry = p+40
Jim = 2p
The sequence is R---> B ---> R -----> B ---> 600
Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)
Now given, 2(2p+120) = 600----> p =90$. Thus A is the correct answer.
Answer: A
Question: In a triangle ABC,point D is on side AB and point E is on side AC,such that BCED is a trapezium.DE:BC =3:5.Calculate the ratio of the area of triangle ADE and the trapezium BCED.
Options:
A)9/16
B)8/16
C)7/16
D)6/16
E)5/16
Rationale: area of tri(ADE)/area of tri(ABC) = DE^2 / BC^2 since tri(ADE) -tri(ABC)
area of tri(ADE)/area of tri(ABC) = 9/25
area of tri(ABC)/area of tri(ADE) = 25/9
area of tri(ABC) = area of tri(ADE) + area of trap(BCDE)
(area of tri(ADE) + area of trap(BCDE))/area of tri(ADE) = 25/9
1 + area of trap(BCDE)/area of tri(ADE) = 25/9
take1on both sides
area of trap(BCDE)/area of tri(ADE) = (25/9) - 1 = 16/9
since question is asking for area of tri(ADE)/area of trap(BCDE) = 9/16
ANSWER:A
Answer: A
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
Options:
A)12
B)14
C)57
D)53
E)47
Rationale: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
27-13=14
Option B
Answer: B
Question: A train running at a speed of 36 km/h passes an electric pole in 15 seconds. In how many seconds will the whole train pass a 380-meter long platform?
Options:
A)47
B)49
C)51
D)53
E)55
Rationale: Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 15 * 10 = 150 m.
The time taken to pass the platform = (150 +380)/ 10 = 53 seconds
The answer is D.
Answer: D
Question: The difference between the place value and the face value of 5 in the numeral 856973 is
Options:
A)973
B)6973
C)5994
D)49995
E)None of these
Rationale: (Place value of 5) - (Face value of 5) = (50000 - 5) = 49995
Answer: Option D
Answer: D
Question: Express a speed of 66 kmph in meters per second?
Options:
A)10.33 mps
B)17 mps
C)97 mps
D)17.33 mps
E)18.33 mps
Rationale: 66 * 5/18
= 18.33 mps
Answer: E
Answer: E
Question: A group of 8 cups need to be arranged. There are 2 blue cups and 2 red cups and the two of the pair of cups must be kept togather. in how many arrangements can the cups be arranged?
Options:
A)A.1296
B)B.1850
C)C.2880
D)D.3546
E)E.4200
Rationale: Glue cupstogether: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each cups within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: C.
Answer: C
Question: Given a number, there is an algorithm described here to find it's sum and number of factors. For example, let us take the number 1225?
Options:
A)1767
B)1800
C)1812
D)1890
E)None
Rationale: Solving for 1225=52×72
Sum of divisors = (ap+1–1)/(a–1)×(bq+1–1)/(b–1)
Here a=5, b=7 prime factors
p=2 and q=2
Sum of divisors = (53–1)/(5–1)×(73–1)/(7–1)
= (124/4)×(342/6)
= (31×57)
= 1767
Option A
Answer: A
Question: Last year, Company X made q dollars in profit. One thrid of the profit went to the company’s founder. The rest was split evenly among his four other partners. In terms of q, how much did each of the other partners receive?
Options:
A)q/4
B)q/5
C)q/8
D)q/6
E)q/7
Rationale: Profit = q
Profit to company founder = q/3
Profit to other partners = 2q/3
Number of other partners = 4
Profit to each partner = (2q/3)/4 = q/6
Answer: D
Answer: D
Question: A and B together can do a piece of work in 5 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
Options:
A)0.35 days
B)0.45 days
C)0.55 days
D)0.25 days
E)0.15 days
Rationale: B = 1/5 – 1/20 =0.15 days
ANSWER:E
Answer: E
Question: For some integer n, n^2 - 5 is divisible by all of the following EXCEPT
Options:
A)41
B)38
C)29
D)30
E)31
Rationale: Hint: n^2-5 (n is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: D
Answer: D
Question: Riya and Priya set on a journey. Riya moves eastward at a speed of 30 kmph and Priya moves westward at a speed of 50 kmph.How far will be priya from Riya after 45 minutes
Options:
A)25kms
B)60kms
C)50kms
D)30kms
E)40kms
Rationale: total eastward distance= 30kmph*3/4hr=22.50 km
total westward distance= 50kmph*3/4hr=37.5 km
total distn betn them= 22.5+37.5=60km
ans 60km
ANSWER:B
Answer: B
Question: Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 10 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
Options:
A)0.1
B)0.6
C)1
D)1.2
E)2
Rationale: Option C
10+40t=50t
t=1
Answer: C