divelab/Sys2Bench huggingface dataset:
Question: A grand father has 3 grand children. Age difference of two children among them is 3. Eldest child age is 3 times the youngest child’s age and the eldest child age is two year more than the sum of age of other two children. What is the age of the eldest child?
Options:
A)22
B)15
C)28
D)26
E)9
Rationale: As the eldest son's age is 3 times that of the youngest, eldest son's age should be a multiple of 3. From the given options take 15 as the eldest son's age. Then youngest son's age becomes 5. But Eldest sons age is 2 more than the sum of the remaining two sons. So Sum of the remaining two sons is 13. So the age of the middle son is 13 - 5 = 8. Which satisfies another condition in the question that the difference between the two sons age is 3. So answer is 15.
Answer:B
Answer: B
Question: A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, in how many ways can he choose the questions?
Options:
A)11340
B)12750
C)40
D)320
E)None
Rationale: Solution: There 10 questions in part A out of which 8 question can be chosen as = 10C8.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 10C5.
Hence, total number of ways,
=10C8*10C5
=[10!/(2!8!)]*[10!/(5!*5)]
= {10*9/2}*{10*9*8*7*6/(5*4*3*2*1)}
= 1140.
Answer: Option A
Answer: A
Question: Find the odd man out. 18, 3, 12, 24, 14, 34, 46
Options:
A)3
B)6
C)24
D)46
E)18
Rationale: Explanation :
3 is the only odd number in the given series
Answer : Option A
Answer: A
Question: A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Options:
A)5/8
B)5/9
C)5/2
D)5/1
E)5/7
Rationale: Two balls can be picked from nine balls in ⁹C₂ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done ⁵C₁ . ⁴C₁ ways.
The required probability = (5 * 4)/⁹C₂
= 20/36
= 5/9
Answer: B
Answer: B
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue?
Options:
A)15/56
B)41/56
C)13/28
D)15/28
E)5/14
Rationale: The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Answer: D
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)9
B)8
C)6
D)1
E)2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: B
Question: What profit percent is made by selling an article at a certain price, if by selling at 1/2rd of that price, there would be a loss of 20%?
Options:
A)20%
B)29%
C)60%
D)27%
E)28%
Rationale: SP2 = 1/2 SP1
CP = 100
SP2 = 80
1/2 SP1 = 80
SP1 = 160
100 --- 160 => 60%
Answer: C
Answer: C
Question: A sequence an is recursively defined where an = 3(an-1-1000) for n > 0. Compute the smallest
integer x such that when a0 = x, an > a0 for all n > 0.
Options:
A)1401
B)1301
C)1201
D)1101
E)1501
Rationale: We want the smallest x such that 3(x - 1000) > x, or 2x > 3000. The smallest
integral x that satisfies this is x = 1501 .
correct answer E
Answer: E
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Options:
A)20 min
B)22 min
C)15 min
D)18 min
E)21 min
Rationale: A
20 min
Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? 20 min
Answer: A
Question: In a two digit number, the digit in the units place is two times the digit in ten's place and sum of the digits is equal to 6. What is the number?
Options:
A)24
B)28
C)32
D)36
E)38
Rationale: Solution
Let the ten digits be x. Then,units digit=2x
Therefore x + 2x = 6
‹=›3x = 6
‹=›x= 2.
So, ten's digit = 2, unit's digit = 4.
Hence, the required number is 24.
Answer A
Answer: A
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Options:
A)22 1/7 %
B)22 8/2 %
C)22 1/9 %
D)22 1/2 %
E)22 2/2 %
Rationale: 9 = (1*40*R)/100
R = 22 1/2 %
Answer: D
Answer: D
Question: Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.19
B)7.59
C)7.16
D)7.15
E)7.12
Rationale: T = (141 + 165)/ (80 + 65) * 18/5
T = 7.59
Answer: B
Answer: B
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 860 in 4 years. The sum is:
Options:
A)s. 650
B)s. 690
C)s. 680
D)s. 700
E)s. 720
Rationale: S.I. for 1 year = Rs. (860 - 815) = Rs. 45.
S.I. for 3 years = Rs.(45 x 3) = Rs. 135.
Principal = Rs. (815 - 135) = Rs. 680.
Answer: Option C
Answer: C
Question: Which of the following is closest to (-7/8)^199？
Options:
A)-1
B)-1/2
C)0
D)1
E)2
Rationale: (-7/8)^4 = 2401/4096 which is already less than 2/3.
For larger exponents, the expression will get closer and closer to zero.
The answer is C.
Answer: C
Question: At a certain bowling alley, it costs $1 to rent bowling shoes for the day and $1.25 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?
Options:
A) 7
B) 8
C) 5
D) 10
E) 9
Rationale: After renting bowling shoes the person is left with $12.80-$1=$11.80, which is enough for 11.8/1.25<10=~9.
Answer:E.
Answer: E
Question: What is the difference between the place values of two sevens in the numeral 54709479 ?
Options:
A)699990
B)99990
C)99980
D)699930
E)None of these
Rationale: Explanation:
Required Difference
= 700000 - 70 = 699930
Answer is D
Answer: D
Question: Find out the square of a number which when doubled exceeds its quarter by 7 ?
Options:
A)16
B)11
C)31
D)29
E)19
Rationale: A
16
Explanation:
Let the number be p, then the square will be p^2
According to question:
2p = (p/4) + 7
=> 8p = p + 28
=> p = 4
p^2 = 4^2 = 16.
Answer: A
Question: An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 68$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?
Options:
A)52
B)37.5
C)92
D)136
E)184
Rationale: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (68 - 40)/(40 - 36) = 28/4 = 7/1 = Number of MicroTron stocks/Number of Dynaco stocks
So for every 7 MicroTron stock, she sold 1 Dynaco stock.
So out of 300 total stocks, (1/7)th i.e. 300/8 = 37.5 must be Dynaco stock.
Answer (B)
Answer: B
Question: If 0 < a < b and k = (2a +5b)/b , which of the following must be true?
Options:
A)k < 2
B)k < 7
C)k < 9
D)k > 9
E)k > 11
Rationale: Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag:Source-Other Please Specify.
As for your question, it is very simple and straightforward with number plug in.
Assume a=1 and b=2 as a<b, you get k = (2+10)/2 = 6. This eliminates all but option B , making it the correct answer.
Answer: B
Question: Convert the 8/26 m/s into kilometers per hour?
Options:
A)3.5 kmph.
B)2.5 kmph.
C)1.2 kmph.
D)1.1 kmph.
E)1.9 kmph.
Rationale: 8/26 m/s = 8/26 * 18/5 = 1 (1/10) = 1.1 kmph.
ANSWER:D
Answer: D
Question: Carol is six times Alice’s age but only twice as old as Betty. Alice is sixty years younger than Carol. How old is Betty?
Options:
A)46
B)39
C)42
D)48
E)36
Rationale: Beyond the obvious Algebra approach to this question, it can also be solved by TESTing THE ANSWERS.
We're told 3 facts about the relative ages of 3 people:
1) Carol's age is 6 times Alice's age
2) Carol's age is 2 times Betty's age
3) Carol is 60 years older than Alice
We're asked for BETTY'S age.
Since Carol is TWICE Betty's age, Betty is clearly younger than Carol, so we'll TEST a smaller answer first.
IF....
Betty = 36
Then Carol = 2(36) = 72
Then Alice = 72 - 60 = 12 AND 72/6 = 12
All of these values mesh perfectly with the facts and with one another, so Betty MUST be 36
E
Answer: E
Question: Which of the following could be the sum of the reciprocals of two prime numbers?
Options:
A)7/13
B)11/12
C)11/30
D)23/50
E)18/77
Rationale: 10/12 it is
18/77=(1/7) + (1/11)
Answer - E
Answer: E
Question: John found that the average of 15 numbers is 40. If 15 is added to each number then the mean of number is?
Options:
A)55
B)45
C)65
D)78
E)64
Rationale: (x+x1+...x14)/15 = 40
55
Option A
Answer: A
Question: If A,B,C are three integers and AB+C is even ; which of the following must be true? A)C is Odd B)B is Odd C)AB is Odd
Options:
A)I only
B)None of the above
C)II only
D)III only
E)I,III only
Rationale: If AB is Odd then C will not even. O+E = O
If AB is even then C will not be odd.
If B is even AB is even always. But If C is Odd E+O = O
If B is Odd AB is even or odd depends on A
None of the above are true.
Answer : B
Answer: B
Question: In a group of 15 people, 8 read English, 7 read French while 3 of them read none of these two. How many of them read French and English both?
Options:
A)2
B)3
C)4
D)7
E)5
Rationale: In the following Venn diagram, F and E represent people who read French and English respectively.
Now, [F+({F ∩ E}) + E] = 15-3 (or) F+E+(F ∩ E) = 12 ......(1) Also, F+(F ∩ E) = 7; E+(F ∩ E) = 8. By adding, F+E+2(F ∩ E) = 15 ---------- (2) By subtracting (1) from (2), we get (F ∩ E) = 3. ∴ 3 of them read both French and English.
Answer:B
Answer: B
Question: The average of first 9 odd numbers is?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Sum of 9 odd no. = 90
Average = 81/9 = 9
ANSWER:E
Answer: E
Question: The maximum number of students among them 100 pens and 50 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
Options:
A)50
B)75
C)69
D)79
E)82
Rationale: number of pens = 100
number of pencils = 50
Required number of students = H.C.F. of 100 and 50 = 50
Answer is A
Answer: A
Question: A can give B 70 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)139.78
B)139.13
C)139.22
D)111.0
E)111.12
Rationale: A runs 1000 m while B runs 930 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/930
= 860.21 m.
B can give C = 1000 - 860.21
=139.78m.
Answer:A
Answer: A
Question: A departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $20,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
Options:
A) $215,000
B) $365,000
C) $115,000
D) $175,000
E) $160,000
Rationale: 20,000 = 0.15 *(50000) + 0.10 (x - 50000)
20000 - 7500 = 0.10 (x-50000)
125000 = x - 50000
x = 1,75,000
Answer : D
Answer: D
Question: A and B invested Rs.4000 and Rs.5000 and they get 20% profit at the end of year. Then share of B is
Options:
A)Rs.1200
B)Rs.1000
C)Rs.1300
D)Rs.1500
E)Rs.1800
Rationale: Total invest is 9000
20% gain of 9000 is 1800
A:B=4:5
B's share will be (5/9)*1800=1000
ANSWER:B
Answer: B
Question: A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.
Options:
A)30
B)40
C)10
D)20
E)50
Rationale: Explanation:
Volume of the block = (6 x 12 x 15) cm3 = 1080 cm3
Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm
= 3 cm.
Volume of this cube = (3 x 3 x 3) cm3 = 27 cm3
Number of cubes = (1080/27) = 40.
Answer: B
Answer: B
Question: A user type a content on 20 sheets, each sheet consist of 55 lines, and each line can have 65 characters. The content is again retyped on a record which is having 71 pages of 65 lines and each line can take 70 characters . How many lines of a record will be free?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: f it is asking for no of pages will be free then
20*55*65= 65*70* (no of page)
no of page= 110/7 = 15.7 = 16 pages
71-16=55(ans)
if it is asking for no of lines will be free in one page then
20*55*65=70*71*(no of lines)
no of lines=14.38= 15 lines
no of lines will be free on each page=65-15=50
ANSWER:C
Answer: C
Question: The length of a rectangle is doubled while its width is tripled. What is the % change in area?
Options:
A)250%
B)300%
C)500%
D)650%
E)700%
Rationale: The original area is L*W
The new area is 2L*3W = 6*L*W = L*W + 5*L*W
The area increased by 500%.
The answer is C.
Answer: C
Question: If
GOOD is coded 164,
BAD is coded 21,
UGLY is coded 260,
then JUMP is coded as ?
Options:
A)230
B)240
C)250
D)260
E)270
Rationale: a=1 , b=2 , c=3 ,....................y=25 , z=26
JUMP = 10+21+13+16 = 60
JUMP is a word of Four letters so multiply it by 4
Therefore , 60*4=240
ANSWER:B
Answer: B
Question: Which letter will come exactly between the tenth letter from your left and the seventh letter from your right. Without changing any order in the original from the alphabet?
Options:
A)o
B)p
C)e
D)r
E)s
Rationale: 10th letter from your left is J
7th letter from your right is T
The mid letter between J and T is O.
ANSWER A
Answer: A
Question: If x and y are positive integers, find which of the following CANNOT be the greatest common divisor of 25x and 20y?
Options:
A)5
B)5(x-y)
C)20x
D)20y
E)35x
Rationale: We are looking for a choice that CANNOT be the greatest common divisor of 25x and 20y ...which means 35x and 20y when divided by the answer choice the quotient should not be a integer.
lets check
a. 5 25x/5 = 5x and 20y/5 = 4y both are integers so eliminate
b. 5(x-y) when x = 2 and y = 1 it could be be the greatest common divisor ..so eliminate
c. 20x when x = 1 its 20 and 20 cannot be the greatest common divisor of 25x and 20y ...
or 25x/20x = 5/4 which is not a integer.
so answer is C.
Answer: C
Question: A club wants to mix 25 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Let number of pounds of 5$ candy to be used be w
6 = (25*8 + 5*w)/(25 +w)
=>150 + 6w = 200 + 5w
=> w = 50
Answer C
Answer: C
Question: A literature panel is to select 4 panelists from a selection of 6 female and 3 male experts. What is the probability that the selected panelists will comprise of exactly 2 males?
Options:
A)4/9
B)2/5
C)3/7
D)1/2
E)5/14
Rationale: We are told that there should be 2 males and 2 females.
Combination approach:
P=C23∗C26/C49=45/126=5/14
Answer: E.
Answer: E
Question: The speed of a boat in upstream is 45 kmph and the speed of the boat downstream is 60 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)7.5 kmph
B)17.5 kmph
C)12.5 kmph
D)5.5 kmph
E)8.5 kmph
Rationale: Speed of the boat in still water = (45+60)/2 = 52.5 kmph. Speed of the stream
= (60-45)/2
= 7.5 kmph.
Answer:A
Answer: A
Question: A function f(x) is said to reflect onitself if, y = f(x) and x = f(y). Which of the following function reflects on itself?
Options:
A)f(x) = (4x + 3) / (3x - 9)
B)f(x) = (4x + 3) / (3x - 2)
C)f(x) = (4x + 3) / (3x - 9)
D)f(x) = (4x + 3) / (3x - 1)
E)f(x) = (4x + 3) / (3x - 4)
Rationale: (a) f(x) = x = f(y)
y = x = f(y) Hence (a) is true.
(b) f(x) = 2x+1x−22x+1x−2 = y
xy - 2y = 2x + 1
xy - 2x = 1 + 2y
x(y - 2) = 1 + 2y
x = 1+2yy−21+2yy−2 Hence (b) is also true.
Similarly if we check for options (c) & (d), they will also hold true, hence t he answer is option (e).
Answer:E
Answer: E
Question: if (x + y)/(2x + y) = 4/7, then find (2x + y)/(3x + y) ?
Options:
A)5/6
B)8/9
C)4/10
D)7/10
E)9/10
Rationale: (x + y)/(2x + y) = 4/7
=> 7x + 7y = 8x + 4y => 3y = x
Now, (2x + y)/(3x + y) = 7y/10y = 7/10.
ANSWER:D
Answer: D
Question: A tempo, while travelling at 70 kmph, uses 30% more petrol than it uses while travelling at 50 kmph for travelling a certain distance. Using one litre of petrol, it can travel 19.5 km at 50 kmph. How far can the tempo travel on 10 litres of petrol at a speed of 70 kmph?
Options:
A)150 kms
B)160 kms
C)170 kms
D)180 kms
E)190 kms
Rationale: @50 kmph , one km distance uses 1/19.5 ltr petrol.
@70kmph, one km dist. uses 1.3/19.5 ltr petrol
Distance travelled with 10 ltrs @ 70kmph = 10*19.5/1.3= 150 kms.
ANSWER:A
Answer: A
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 120 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)76 kmph
C)12 kmph
D)35 kmph
E)15 kmph
Rationale: Speed of the boat in still water
= (50+120)/2
= 170 kmph. Speed of the stream
= (120-50)/2
= 35 kmph.
Answer:D
Answer: D
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Options:
A)6 kmph
B)7 kmph
C)8.5 kmph
D)8 kmph
E)9 kmph
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
ANSWER:A
Answer: A
Question: If x is an integer and 2.134 × 10^x is less than 210,000, what is the greatest possible value for x?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: 21340 * 10^-4 * 10^x < 210,000, x=4
because the next zero on the right side will make 21,340 > 210,000
Answer D,
Answer: D
Question: Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?
Options:
A)$21,000
B)$18,000
C)$15,000
D)$ 4,500
E)$4,000
Rationale: 360 + 0.06 (x-1000) = 0.08x
or 360 -60 = 0.08x
or 300/0.02 = x
or 15000 =x
Answer : C
Answer: C
Question: Antony has s pairs of shoes, which is 1/2 as many as Steve and thrice as many as Stephen. In terms of s, how many pairs of shoes do the three of them have combined?
Options:
A)14/3*s
B)10/3*s
C)4s
D)5s
E)11/3*s
Rationale: == s +2s + s/3 ==> 3s + 1/3 s = 10/3*s
Ans .B
Answer: B
Question: The greatest number of four digits which is divisible by 16,24,40 and 72 is:
Options:
A)9020
B)9400
C)9360
D)9600
E)9740
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 16, 24, 40 and 72 is 720.
On dividing 9999 by 720, the remainder is 639.
Required number (9999 - 639) = 9360.
Answer: Option C
Answer: C
Question: A man can row 4 kmph in still water. When the river is running at 1.8 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)7.13
B)6.19
C)4.12
D)3.19
E)4.21
Rationale: M = 4
S = 1.8
DS = 5.8
US = 2.2
x/5.8 + x/2.2 = 1
x = 1.59
D = 1.59 * 2 = 3.19
Answer: B
Answer: B
Question: John started a business investing Rs. 70,000. Rose joined him after six months with an amount of Rs.1,05,000 and Mary joined them with Rs. 1.4lakhs after another 6 months. The amount of profit earnedshould be distributedin what ratio among John, Rose and Mary respectively, 3years after John started the business?
Options:
A)10 : 11 : 13
B)9 : 15 : 16
C)12 : 15 : 16
D)14 : 15 : 18
E)12 : 15 : 20
Rationale: John : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16
C
Answer: C
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
Options:
A)176 km
B)224 km
C)168 km
D)197 km
E)258 km
Rationale: Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x
= 224 km.
Answer: B
Answer: B
Question: In how many ways can 4 arts and 4 science students be arranged in a row so that the arts and the science students are placed alternately?
Options:
A)288
B)185
C)326
D)576
E)360*120
Rationale: The four art students can be arranged in those 4 A-slots in 4! = 24 ways.
The four science students can be arranged in those 4 S-slots in 4! = 24 ways.
Total arrangements = 24*24 = 576
Answer =(D)
Answer: D
Question: The variables a and b are non-zero integers V. If a = 2b^3/c, what happens to c when a is halved and b is doubled?
Options:
A)c is not changed.
B)c is halved.
C)c is doubled.
D)c is multiplied by 4.
E)c is multiplied by 16.
Rationale: a = 2b^3/c
c = 2b^3/a
when a is halved and b is doubled
c =2(2b)^3/(a/2)
c=16*2b^3/a
Ans. E c is multiplied by 16.
Answer: E
Question: The residents of the town R participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town R, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Options:
A)- 30
B)- 20
C)- 18
D)- 12
E)- 6
Rationale: (21-6*2)<number of hours that Pat watched television last week <(21-6*1)
=9<P<15
Only option E (12) satisfies this condition.
Answer: E
Question: How many different arrangements of A, B, , D, and E are possible where A is not adjacent to B and D is not adjacent to E?
Options:
A)96
B)48
C)8
D)30
E)1
Rationale: So you have A,B,,D,E
five possible ways to arrange it = 4! = 24
AB cannot be adjacents neither DE:
(AB),,D,E = 3! = 6x 2(because it can be (AB) or (BA) ) = 12
A,B,,(DE) = 3! = 6 x 2 = 12
To get rid of the double counting:
(AB),(DE) = 2! x 4 = 8
(Four possible ways to arrange it)
24 -12-12+8 =8 possible ways
C
Answer: C
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 10 minutes 8 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
Options:
A) 3%
B) 5%
C) 8%
D) 10%
E) 12%
Rationale: Bob's time = 640 secs.
His sis' time = 608 secs.
Percent increase needed = (640-608/640) * 100 = 32/640 * 100 = 5%. Ans (B).
Answer: B
Question: 60 + 5 * 12 / (180/3) = ?
Options:
A)23
B)78
C)27
D)61
E)81
Rationale: Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.
Answer:D
Answer: D
Question: 504 can be expressed as a product of primes as
Options:
A)2 × 2 × 3 × 3 × 7 × 7
B)2 × 3 × 3 × 3 × 7 × 7
C)2 × 2 × 2 × 3 × 3 × 7
D)2 × 3 × 3 × 3 × 3 × 7
E)None of these
Rationale: Explanation:
It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7
Answer: Option C
Answer: C
Question: A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train is :
Options:
A)70 m
B)80 m
C)90 m
D)100 m
E)None
Rationale: Solution
Let the length of the train be x metres .
∴ x+162/18 =x+120/15 =15(x+162) =18(x+120) = x=90m
Answer C
Answer: C
Question: Four-fifths of three-eighths of a number is 24. What is 250 per cent of that number?
Options:
A)100
B)160
C)120
D)200
E)None of these
Rationale: Let the number = x.
4⁄5 × 3⁄8x = 24 or x = 24×2×5/3=80
∴ 250 per cent of the number = 250⁄100 × 80 = 200
Answer D
Answer: D
Question: If x is an integer and 2.134 × 10^x is less than 2,100,000, what is the greatest possible value for x?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: If x=6
2.134 × 10^6 = 2,134,000 > 2,100,000
So, x = 5
Answer : C
Answer: C
Question: A can do a piece of work in 8 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?
Options:
A)2 days
B)5 days
C)6 days
D)7 days
E)11 days
Rationale: B's 9 day's work = 9 x (1/12) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/4 work is done by A in = 8 x (1/4) = 2 days.
answer : A
Answer: A
Question: You enter a weight loss challenge game and manage to lose 13% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?
Options:
A)13%
B)9.22%
C)11.26%
D)14%
E)12%
Rationale: (100%-13%)*(100%+2%) = 0.87*1.02 = 11.26%
The weigh in records your weight loss at 11.26%!
The Answer is C
Answer: C