mathewhe/aqua_rat huggingface dataset:
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 16 days. In how many days Peter complete the work separately.
(A) 26 days
(B) 27 days
(C) 23 days
(D) 35 days
(E) 40 days
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 16 days which means that the whole job(1) can be completed in X days.
<=> 8/20->16 <=> X=16/(8/20)=40 Thus the answer is E.
Answer: (E) 40 days
Question: Anita, Indu and Geeta can do a piece of work in 18 days, 27 days and 36 days respectively. They start working together. After working for 4 days. Anita goes away and Indu leaves 7 days before the work is finished. Only Geeta remains at work from beginning to end. In how many days was the whole work done?
(A) 13 days
(B) 16 days
(C) 18 days
(D) 11 days
(E) 12 days
Rationale: B
16 days
4/18 + (x -7)/27 + x/36 = 1
x = 16 days
Answer: (B) 16 days
Question: The sale price sarees listed for Rs.560 after successive discount is 20% and 30% is?
(A) 321
(B) 314
(C) 316
(D) 265
(E) 162
Rationale: Explanation:
560*(80/100)*(70/100) = 314
Answer: B
Answer: (B) 314
Question: For a positive integer n, define S(n) to be the sum of the positive divisors of n. Which of the
following is the smallest?
(A) S(2010)
(B) S(2011)
(C) S(2012)
(D) S(2013)
(E) S(2014)
Rationale: 2011 is prime, so that S(2011) = 1 + 2011 = 2012, the smallest.
But this answer can be verified without checking that 2011 is prime. Observe that
S(2010) > 2010 + 1005 > 3000
S(2013) > 2013 + 671 > 2600
and S(2012) and S(2014) are also larger than 3000.
Check by hand that 2, 3, 5, 7, and 11 do not divide 2011, and so if 2011 is not prime, then it
is a product of two primes p and q. If p 6= q, then
S(2011) = 2011 +
2011/p
+
2011/q
+ 1;
and p and q are greater than 11, so that this is smaller than 2600. If p = q then this is smaller
still.
correct answer B
Answer: (B) S(2011)
Question: If the cost price of 15 articles is same as the selling price of 25 articles. Find the gain or loss percentage?
(A) 30% Gain
(B) 30% Loss
(C) 40% Gain
(D) 40% Loss
(E) 50% Loss
Rationale: Explanation:
15 cp = 25 sp
Cost price CP = 25
Selling price SP = 15
Formula = (SP-CP)/CP * 100 = (15 - 25)/25 * 100 = 40 % Loss
Answer: Option D
Answer: (D) 40% Loss
Question: What is the sum of the multiples of 4 between 63 and 151 inclusive?
(A) 2240
(B) 2250
(C) 2310
(D) 2330
(E) 2332
Rationale: the fastest way in an AP is to find the average and multiply with total integers..
between 63 and 151, the smallest multiple of 4 is 64 and largest =148..
average=(64+148)/2=106..
total numbers = (148-64)/4 + 1= 21+1=22..
sum=22*106=2332
ans E
Answer: (E) 2332
Question: If a sum of money at simple interest doubles in 6 years, it will become 4 times in
(A) 15years
(B) 16years
(C) 11years
(D) 18years
(E) 12years
Rationale: Explanation:
let sum =x . s.i.=x
rate =(100*x)/(x*6)=50/3%
now ,sum =x, s.i= 3x, rate =50/3%
time =(100*3x)/(x*50/3) = 18 years
Answer: D
Answer: (D) 18years
Question: A photograph measuring 8.5 by 7.5 cm is to be enlarged. If the enlargement of the longer side is 13.6 cm, what is the length of the smaller side?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Sol.
= (13.6 ÷ 8.5) × 7.5
= 12 cm.
Answer : C
Answer: (C) 12
Question: In how many ways the letters of the word RAIMBON be arranged?
(A) 4678
(B) 8754
(C) 5040
(D) 8658
(E) 8754
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
C)
Answer: (C) 5040
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6.6 m x 22.5 cm?
(A) 6400
(B) 6410
(C) 6440
(D) 6500
(E) 7040
Rationale: Number of bricks = Volume of Wall/Volume of Bricks
=800x660x22.5/25x11.25x6= = 7040
answer :E
Answer: (E) 7040
Question: Two cylinders of the radius in the ratio 3 : 5 and heights in the ratio 10 : 9. Then find the volumes ratio?
(A) 4:5
(B) 1:5
(C) 3:5
(D) 1.5:5
(E) 2:5
Rationale: πR(power2)H : πr(power2)h
9 × 10 : 25 × 9
90 : 225
2 : 5
Answer is E.
Answer: (E) 2:5
Question: ind the ratio of the curved surfaces of two cylinders of same heights if their radii are in the ratio 1:2?
(A) 18 kmph
(B) 19 kmph
(C) 24 kmph
(D) 17 kmph
(E) 16 kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8)
= 24 kmph
Answer: C
Answer: (C) 24 kmph
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:30
(C) 39:47
(D) 39:45
(E) 39:41
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: (A) 39:40
Question: Maru obtained 66, 65, 82, 67 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 71
(B) 38
(C) 39
(D) 37
(E) 75
Rationale: Average = (66 + 65 + 82 + 67 + 75)/5
= 71.
Answer: A
Answer: (A) 71
Question: A is twice as good as B. And together they finish a piece of work in 18days. In how many days will A alone finish the work
(A) 25
(B) 27
(C) 15
(D) 18
(E) 21
Rationale: (A's 1day work):(B's 1day work) = 2:1
A+B 1day work = 1/18
A's 1day work = (1/18)*(2/3) = 1/27
A alone can finish the work in 27 days
Answer is B
Answer: (B) 27
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
(A) 22777
(B) 28877
(C) 26888
(D) 28800
(E) 67881
Rationale: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
Answer:D
Answer: (D) 28800
Question: In track last week, the boys ran 27 laps. The girls ran 9 more
laps. Each lap is a three-fourth of a mile. How many miles did the girls run?
(A) 24 miles
(B) 25 miles
(C) 26 miles
(D) 27 miles
(E) 28 miles
Rationale: The girls ran 27 + 9 = 36 laps. 36 x3/4 = 108/4, which reduces to 27.
The girls ran 27 miles
correct answer D
Answer: (D) 27 miles
Question: Dan can do a job alone in 15 hours. Annie, working alone, can do the same job in just 10 hours. If Dan works alone for 3 hours and then stops, how many hours will it take Annie, working alone, to complete the job?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Dan can complete 1/15 of the job per hour.
In 3 hours, Dan completes 3(1/15) = 1/5 of the job.
Annie can complete 1/10 of the job per hour.
To complete the job, Annie will take 4/5 / 1/10 = 8 hours.
The answer is D.
Answer: (D) 8
Question: Hannah and Glen will throw three dice each. The score is the sum of points on all three dice. If Hannah scores 3 in her attempt, what is the probability that Glen will outscore Hannah in his attempt?
(A) 5/6
(B) 35/36
(C) 71/72
(D) 215/216
(E) 431/432
Rationale: The total number of ways the dice can land is 6*6*6=216.
There is only 1 way that Glen can get a score of 3 = 1+1+1
Glen wins for any other outcome.
P(Glen wins)=1-1/216=215/216
The answer is D.
Answer: (D) 215/216
Question: A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train.
(A) 150
(B) 278
(C) 179
(D) 250
(E) 191
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 15 = 250 meter
Answer:D
Answer: (D) 250
Question: If each year the population of the country grows by 40%, how many years will elapse before the population of the country doubles?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Till Year 2000, population is 100 .
Year 2001: Population becomes 140 ............. 1 Year elapsed
Year 2002: Population becomes 196 ............. 2 Year elapsed
Year 2003: Population > 200 .................. 3 year elapsed
Answer:A
Answer: (A) 3
Question: If 0.75 : x :: 5 : 8, then x is equal to:
(A) 1.12
(B) 1.2
(C) 1.25
(D) 1.3
(E) none
Rationale: (x * 5) = (0.75 * 8)
x = 6/5
x = 1.20
Answer = B
Answer: (B) 1.2
Question: The average age of a group of n people is 14 years old. One more person aged 32 joins the group and the new average is 15 years old. What is the value of n?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: 14n + 32 = 15(n+1)
n = 17
The answer is E.
Answer: (E) 17
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 37 km/hr
(B) 53 km/hr
(C) 36 km/hr
(D) 26 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 8 = 45 => x = 53 km/hr.
Answer:B
Answer: (B) 53 km/hr
Question: If in coded language
23 = 10
72 = 63
65 = 66
84 = 96
Then
97 = ?
(A) 141
(B) 142
(C) 143
(D) 144
(E) 145
Rationale: 2x(2+3)=10
7x(7+2)=63
6x(6+5)=66
8x(8+4)=96
9x(9+7)=144
ANSWER:D
Answer: (D) 144
Question: A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?
(A) 140
(B) 388
(C) 238
(D) 119
(E) 112
Rationale: when folded along the breadth
we have 2(l/2 +b) = 34 or l+2b = 34...........(1)
when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2)
from 1 &2 we get l=14 and b=10
Area of the paper = 14*10 = 140 sq cmV
Answer: A
Answer: (A) 140
Question: Sequence of numbers are 1, 11, 21, 1211, 111221.
What will be the next one in the above sequence?
(A) 223461
(B) 443576
(C) 532457
(D) 126434
(E) 312211
Rationale: E
312211
It is a strange sequence. Each number describes the resemblance of the previous one, except the first one.
11 describes the previous '1' which contains one '1'
21 describes the previous '11' which contains two '1'
1211 describes the previous '21' which contains one '2' and one '1'
111221 describes the previous '1211' which contains one '1', one '2' and two '1'.
So the next sequence will be 312211, that is the previous '111221' contains three '1', two '2' and one '1'.
Answer: (E) 312211
Question: A family consists of two grandparents, two parents and six grandchildren. The average age of the grandparents is 65 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of family?
(A) 10/6years
(B) B)31
(C) C)30
(D) D)33
(E) E)35
Rationale: Required average
= (65 x 2 + 35 x 2 + 6 x 6 )/(2 + 2 + 6)
= (134 + 70 + 18)/10
= 236/10
= 23 10/6years.
Answer is A
Answer: (A) 10/6years
Question: The guidelines at a certain college specify that for the introductory English class, the professor may choose one of five specified novels, and choose two plays from a list of 5 specified plays. Thus, the reading list for this introductory class has one novel and two plays. How many different reading lists could a professor create within these parameters?
(A) 50
(B) 55
(C) 60
(D) 65
(E) 70
Rationale: 5C1*5C2 = 5*10 = 50
The answer is A.
Answer: (A) 50
Question: Difference between the length &breadth of a rectangle is 26 m. If its perimeter is 208 m, then its area is?? We have: (l - b) = 26 and 2(l + b) = 208 or (l + b) = 104?
(A) 2525 m^2
(B) 2625 m^2
(C) 2535 m^2
(D) 2553 m^2
(E) 2635 m^2
Rationale: Solving the two equations, we get: l = 65 and b = 39.
Area = (l x b) = (65 x 39) m2 = 2535 m^2
C
Answer: (C) 2535 m^2
Question: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the following must be true of N?
(A) 5/6 < N < 10/11
(B) 21/10 < N < 9/2
(C) 5 < N < 5 1/11
(D) 5 < N < 5 5/11
(E) 30 < N < 60
Rationale: Each fraction is close to 1 so we know that the sum will be less than 6.
Lets just say they're each 1 so N=6.
But now we have to subtract the difference
1/6+1/7+1/8+1/9+1/10+1/11.
We can estimate these each as 1/10-->5/10 which is 1/2.
D is the closest representation
Answer: (D) 5 < N < 5 5/11
Question: 14, 23, 32, 41, 50, 59, …
In the sequence above, each term is 9 more than the previous term. What is the 41st term W of the sequence?
(A) 360
(B) 365
(C) 369
(D) 374
(E) 383
Rationale: First term , a= 14
Common difference , d = 9
nth term , tn = a + (n-1)d
41st term W , t41 = a+ 40*d = 14 + 40*9 = 374
Answer D
Answer: (D) 374
Question: How many 3-digit numbers are completely divisible 6 ?
(A) 100
(B) 150
(C) 200
(D) 250
(E) 300
Rationale: 3-digit number divisible by 6 are: 102, 108, 114,... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then tn = 996.
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150
Number of terms = 150.
B)
Answer: (B) 150
Question: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. Find the diameter of each sphere.
(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm
(E) 12 cm
Rationale: Explanation:
In this type of question, just equate the two volumes to get the answer as,
Volume of cylinder =πr2h
Volume of sphere =43πr3
=>12∗4/3πr3=πr2h
=>12∗4/3πr3=π∗8∗8∗2
=>r3=8∗8∗2∗3/12∗4
=>r3=8
=>r=2cm
=>Diameter =2∗2=4cm
Option A
Answer: (A) 4 cm
Question: A school’s annual budget for the purchase of student computers increased by 20% this year over last year. If the price of student computers increased by 10% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
(A) 9%
(B) 9.09%
(C) 10%
(D) 10.09%
(E) 11.09%
Rationale: Pick numbers.
Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $120, price = $1.1 --> the number of computers purchased = 120/1.1 = ~109.09
Increase in the number of computers purchased = 9.09%
Answer: B.
Answer: (B) 9.09%
Question: There are 4 gold chain. 1 has 5links, other has 4 links and the other 2 have 3 links.
goldsmith takes 50 paise to open the link and 1.00/- to attach the link. what is least cost to
bake whole bracelet.
(A) 3.50 rupees
(B) 4.50 rupees
(C) 4.80 rupees
(D) 5.50 rupees
(E) 6.50 rupees
Rationale: Let,the shape of the bracelet is closed circle.[It is supposed to assume]
gold chain with 5 links: A_ _ _ _ _B
gold chain with 4 links: C_ _ _ _D
gold chain with 3 links: E_ _ _F
gold chain with 3 links: G_ _ _H
We,generally hold a common notion that since there are 4 gold chains and since we are to make a closed circular shaped bracelet, so,we have to join the ends namely :(B,C),(D,E),(F,G),(H,A),i.e, total 4 links have to be broken and further joined,i.e, total cost will then be 4(1+.50)= 6 rupees.
But,now we will tackle the problem in a different way.
Let, all the 3 links of GH chain are broken.
Then,
with the help of 1st broken link, B and C ends are joined.
with the help of 2nd broken link, D and E ends are joined.
and,
With the help of the remaining broken link, F and A ends are joined.
So, the above mentioned method explains us that breaking only 3 links and subsequently joining two free ends with each link facilitates us to make a whole closed circular shaped bracelet.
Therefore,the cost in this case : 3*(1+.50) = 3*(1.50)=4.50 rupees;
So,evidently,the least cost to make the whole bracelet :4.50 rupees .
ANSWER:B
Answer: (B) 4.50 rupees
Question: Average age of A and B is 24 years and average age of B, C and D is 22 years. The sum of the ages of A, B, C and D is
(A) 76 years
(B) 30 years
(C) 77 years
(D) 88 years
(E) 56 years
Rationale: Let their ages 10 years ago is x, 2x and 3x years.
10 + 2x + 10 + 3x + 10 = 90 hence x= 10
B’s present age = (2x + 10) =30 years
Answer: B
Answer: (B) 30 years
Question: Jake, Lena, and Inna need to drive home from a corporate reception in an SUV that can seat 5 people. If only Inna or Jake can drive, how many seat allocations are possible?
(A) 24
(B) 42
(C) 120
(D) 360
(E) 720
Rationale: 3 people ,5 seats, only 2 can drive
if inna is in one seat remaining, 2 people can be arranged in 2p2 i.e 2! =2 ways
since any one can drive total ways = 2 *2= 4 ways
4 seats can be chosen out of remaining 5 seats in 5c4 ways = 5!/(3!*2!)= 6 ways
4*6=24
A
Answer: (A) 24
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.8
(B) 1.5
(C) 1.9
(D) 1.2
(E) 1.1
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: (B) 1.5
Question: In a urban village of india named "owlna" , 80% people have refrigerator , 82% people have television , 70% people got computers and 75% got Air-conditionor. how many people(minimum) got all these luxury.
(A) 3%
(B) 8%
(C) 7%
(D) 10%
(E) 15%
Rationale: C
7%
100 - [ (100-80)+(100-82)+(100-70) +(100-75)]
=100-(20+18+30+25)
=100-93
Answer: (C) 7%
Question: If x - 8 = -|x|, then x=?
(A) 2
(B) -4
(C) 4
(D) 3
(E) 5
Rationale: x - 8 = -|x| ...(given)
x^2 - 16x + 64 = x^2
0*x^2 + 16*x -64 = 0 ....(by solving above eq. we get) , x = 4 ===> Ans - C
Answer: (C) 4
Question: In a division, divident is 760, divisior is 36 and quotient is 21. Find the remainder.
(A) A)4
(B) B)3
(C) C)2
(D) D)5
(E) E)6
Rationale: Explanation:
760 = 36 x 21 + r
760 = 756 + r
r = 760 - 756 = 4
Answer: Option A
Answer: (A) A)4
Question: The simple interest accrued on an amount Rs.10,000 at the end of two years is same as the compound interest on Rs.8,000 at the end of two years. The rate of interest is same in both the cases. What is the rate of interest?
(A) 22
(B) 77
(C) 66
(D) 50
(E) 88
Rationale: Given that Rs.10,000 is invested in S.I for two years and Rs.8,000 in C.I for two years
=> C.I - S.I
=> 8,000 { [1 + r/100]2 - 1} = (10,000)2r /100
=> 8{ 1 + 2r/100 + r2 / (100)2 - 1} = r/5
=> 16r/100 + 8r2/(100)2 = 20r/100
=> 4r/10 = 8r2/(100)2
=> 8[r/100]2 - 4r/100 = 0
=> r/100 {8r/100 -4} = 0
=> r = 0% of 50%
Since r!= 0%, r =50%
Answer:D
Answer: (D) 50
Question: If y = 1296 * 125 * 4096 / 25, How many digits are in y,
(A) 4
(B) 8
(C) 2
(D) 6
(E) 3
Rationale: y = 1296 * 125 * 4096 / 25
y = 8^4 * 5^3 * 6^4 / 5^2
y = 48^4 * 5
y = 26542080
Ans: B
Answer: (B) 8
Question: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $8.64 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discount rates is 22 percent, what is the discount rate on Pony jeans?
(A) 8%
(B) 10%
(C) 11%
(D) 12%
(E) 14%
Rationale: Let x be the discount on Pony jeans. Then 0.22-x is the discount on Fox jeans.
3(0.22-x)(15) + 2x(18) = 8.64
9.9 - 45x + 36x = 8.64
9x = 1.26
x = 0.14
The answer is E.
Answer: (E) 14%
Question: Of 100 applicants for a job, 50 had at least 5 years of prior work experience, 40 had advanced degrees, and 10 had at least 5 years of prior work experience and advanced degrees. How many of the applicants had neither 5 years of prior work experience nor advanced degrees?
(A) 30
(B) 15
(C) 20
(D) 34
(E) 22
Rationale: Had advanced degrees and 5 years work experience: 10
Only had 5 years work experience: 50-10 = 40
Only had advanced degrees: 40-10 = 30
100-10-40-30=20
Answer: C
Answer: (C) 20
Question: An urn contains g green marbles and b blue marbles. If 3 green marbles and 7 blue marbles are added, and then one marble is selected at random from the urn, what is the probability that a blue marble will be drawn?
(A) b/(b+g)
(B) (b+5)/(g+3)
(C) (b+5)/(b+g+8)
(D) (b+5)/(b+g+3)
(E) b+7/(b+g+10)
Rationale: no of fav outcomes i.e. blue MArbles = b+5
Total no of outcomes i.e. total Marbles = (b+7)+(g+3)= b+g+10
probability = (b+7) /(b+g+10)
Answer E
Answer: (E) b+7/(b+g+10)
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 12%?
(A) 20%
(B) 25%
(C) 13 1/30%
(D) 32%
(E) 13%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 88
2/3 SP1 = 88
SP1 = 132
100 --- 32 => 32%
ANSWER:D
Answer: (D) 32%
Question: In a group of 6 male and 4 female, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 200
(B) 209
(C) 207
(D) 300
(E) 350
Rationale: req no = 6C1*4C1 + 6C2*4C1 + 6C4
==6C1+4C1 + 6C2+4C2 + 6C3*4C1 + 6C4
(6*4) + (6*5/2*1 * 4*3/2*1) + 6*5*4/3*2*1*4 + 6*5/2*1
==> 209
ANSWER B
Answer: (B) 209
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit?
(A) 39:40
(B) 39:86
(C) 39:18
(D) 39:10
(E) 32:40
Rationale: 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
Answer: (A) 39:40
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 0
II. y = 0
III. x = -y
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
Rationale: Re-arrange equation: x^2 - xy = 0 => x*(x-y) = 0
Therefore, either x=0 or x=y. We know that x and y are different, so x must be equal to 0.
ANSWER:A
Answer: (A) I only
Question: Each factor of 230 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 46?
(A) 1/16
(B) 5/42
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: so the # of factors 230 has 8 (see below);
so out of 8 factors only two are multiples of 46: 46 and 230, itself;
So, the probability is 2/8=1/4.
Answer: E.
Answer: (E) 1/4
Question: A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 1 specified cars. In how many ways cars can be arranged?
(A) 1210
(B) 120
(C) 1500
(D) 1640
(E) 1440
Rationale: we arranged 1 specified cars in 1 slots = 1!
remaining 5 cars in 5 slots = 5!
number of ways = 1!*5! = 120
correct option is B
Answer: (B) 120
Question: A class of six students has to split into two indistinguishable teams of three people. Compute
the number of distinct team arrangements that can result.
(A) 2 distinct teams.
(B) 4 distinct teams.
(C) 10 distinct teams.
(D) 8 distinct teams.
(E) 7 distinct teams.
Rationale: Consider one specific person of the six students. There are
(5
2)
to choose the 2
partners on his team. Hence, there are
(5
2)
= 10 distinct teams.
correct answer C
Answer: (C) 10 distinct teams.
Question: If x is divisible by 2, 14, and 10, which of the following must be the least multiple of x?
(A) 308
(B) 154
(C) 70
(D) 44
(E) 21
Rationale: We are looking for the LCM (which is not 0) of 2, 10 = 2*5, 14 = 2*7:
2 * 5 * 7 = 70
The answer is C.
Answer: (C) 70
Question: A person distributed 20% of his income to his 3 children each. He deposited 30% of his income to his wife's account. He donated 5% of remaining amount to an orphan house.Finally he has $50000. Find his total income?
(A) A)452000
(B) B)562000
(C) C)800000
(D) D)1000000
(E) E)652000
Rationale: 3 children got = 3*20% = 60%
wife got = 30%
orphan house = 5%
total = 60+30+5 = 95%
remaining = 100-95 = 5%
5% = 50000
100% = 50000*100/5 = $1000000
Answer is D
Answer: (D) D)1000000
Question: In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B can give C in a game of 60 ?
(A) B can give C 1 points
(B) B can give C 4 points
(C) B can give C 2 points
(D) B can give C 6 points
(E) B can give C 8 points
Rationale: A: B = 80 : 75, A : C = 80 : 65.
B/C = ( B/ A * A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5
Therfore ,In a game of 60, B can give C 8 points.
Answer is E.
Answer: (E) B can give C 8 points
Question: If c equals the sum of the even integers from 2 to 504, inclusive, and m equals the sum of the odd integers from 1 to 297, inclusive, what is the value of c + 2m?
(A) 85957
(B) 108158
(C) 299376
(D) 107860
(E) 150788
Rationale: Use following formulae for such problems:
Sum of evenly spaced integers = (# of integers)*(mean of integers)
# of integers = [(last - first)/2] + 1
Mean of integers = (last + first)/2
In above problem:
# of integers = [(504 - 2)/2] + 1= 252 and [(297-1)/2]+ 1 = 149
Mean of integers = (504 + 2)/2 = 253 and (297 + 1)/2 = 149
Sum of integers = (252*253) = 63756 and (149*149) = 22201
Thus their sum (c + 2m) = 63756 + (2 * 22201) = 108258
ANSWER:B
Answer: (B) 108158