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mathematics | There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.
How much water evaporated? | [
"20",
"30",
"40",
"50",
"10"
]
| In the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.
The answer is: D | D |
mathematics | A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 420. Find the sum? | [
"s. 5000",
"s. 7000",
"s. 14000",
"s. 17000",
"s. 27000"
]
| Let the sum be Rs. x.
(x * 15 * 2)/100 - (x * 12 * 2)/100 = 420
=> 30x/100 - 24x/100 =420
=> 6x/100 = 420
=> x = 7000.
ANSWER:B
The answer is: B | B |
mathematics | The average mark of a class of twenty students is 64. If three students whose marks are 32,28 and 34 are removed , then find the approximate average mark of the remaining students of the class. | [
"71",
"74",
"57",
"70",
"72"
]
| Total mark of 20 students = 64*20 = 1280,
Total mark after the removal of 3 students = 1280 –(32 +28+34 )
= 1280 – 94 = 1186
Approximate average mark = 1186/(20-3)
= 1186/ 17
= 70
ANSWER:D
The answer is: D | D |
mathematics | Calculate the amount that an investor needs to be invest to earn $460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9% compounded semi-annually? | [
"7,000",
"4,000",
"6,000",
"5,000",
"8,000"
]
| the approach is substitution,
our interest requirement is 460 after 12 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields 460 in 12 months
5,000 yielded $460
using the formula
A = P(1 + r/n)nt
hence answer is D
The answer is: D | D |
mathematics | Find the area of circle whose radius is 7m? | [
"138",
"154",
"288",
"280",
"371"
]
| 22/7 * 7 * 7
= 154
Answer:B
The answer is: B | B |
mathematics | Due to construction, the speed limit along an 5-mile section of highway is reduced from 40 miles per hour to 22 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | [
"A) 3.12",
"B) 8",
"C) 10",
"D) 15",
"E) 6.13"
]
| Old time in minutes to cross 5 miles stretch = 5*60/40 = 5*3/2 = 7.5
New time in minutes to cross 5 miles stretch = 5*60/22 = 5*30/11 = 13.63
Time difference = 6.13
Ans:E
The answer is: E | E |
mathematics | What is the sum of all the multiples of 10 between 0 and 85? | [
"500",
"620",
"450",
"360",
"440"
]
| The multiples of 10 between 0 and 85 are 10, 20, 30, 40, 50, 60, 70, 80. If these are all added together, the result is 360.
Final Answer:
D
The answer is: D | D |
mathematics | In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ? | [
"120960",
"135650",
"115850",
"142560",
"185260"
]
| In the word 'MATHEMATICS' we treat the two vowels AEAI as one letter. Thus,we have MTHMTCS (AEAI)
Now, we have to arranged 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters= 8!/(2!)(2!)=10080.
Now AEAI has 4 letters in which A occurs 2 times and the rest are different.
number of ways of arranging these letters =4!/2!=12.
Required number of ways =(10080*12)=120960.
Answer is A
The answer is: A | A |
mathematics | A number when divided by 100 leaves 11 as a remainder. What will be the remainder if the number is divided by 11? | [
"11",
"1",
"2",
"3",
"21"
]
| Let 100+11=111
111 divided evenly by eleven leaves a remainder of one.
Correct answer is B.
The answer is: B | B |
mathematics | What is the sum of all possible 3-digit numbers that can be constructed using the digits 1, 3, and 4 if each digit can be used only once in each number? | [
"1443",
"1554",
"1665",
"1776",
"1887"
]
| There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(111) + 2(333) + 2(444) = 1776
The answer is D.
The answer is: D | D |
mathematics | If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 4 and 5K + 1 is 63, what is the value of K? | [
"22 10/11",
"15 3/4",
"22",
"23",
"25 3/10"
]
| K + 2K +3 + 3K - 4 + 5K +1 = 11K
(11K -1)/4 = 63
11K = 63 * 4 = 252
K = 252 / 11 = 22 10/11
Answer A.
The answer is: A | A |
mathematics | A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995? | [
"5%",
"18%",
"33%",
"35%",
"38%"
]
| Soln:-
Profit in 1995 - 100
Profit in 1996 - 115
%increase Profit in 1997 in comparison to 1995 = 15 + 115*20%= 38%
ANSWER:E
The answer is: E | E |
mathematics | Which of the following integers is a divisor of(15!+15)? | [
"15",
"14",
"13",
"7",
"2"
]
| When we say 15!, it just means 1*2*3*4*5*...*13*14*15
So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 15) = 15 (1*2*3*4*5*...*12*13*14 + 1) We obtain this by taking 15 common.
Hence 15 is definitely a divisor of (15! + 15).
A
The answer is: A | A |
mathematics | If A lends Rs.2000 to B at 15% per annum and B lends the same sum to C at 17% per annum then the gain of B in a period of 4 years is? | [
"155",
"162",
"157.5",
"160",
"157.12"
]
| (2000*2*4)/100
=> 160
Answer: D
The answer is: D | D |
mathematics | The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 2years ago? | [
"152460",
"214560",
"160000",
"210000",
"200000"
]
| population 2 years ago = 176400/(1 + 5/100)^2
= 176400* 20/21 * 20/21
=160000
Answer is C
The answer is: C | C |
mathematics | In how many years will a sum of money doubles itself at 5% per annum on simple interest? | [
"20",
"25",
"15",
"10",
"30"
]
| P = (P*5*R)/100
R = 20%
ANSWER A
The answer is: A | A |
mathematics | There are 13 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have? | [
"17/52",
"14/39",
"12/31",
"9/23",
"7/17"
]
| P(first stamp is different) = 8/13
P(second stamp is different) = 7/12
P(both stamps are different) = 8/13*7/12 = 14/39
The answer is B.
The answer is: B | B |
mathematics | 1=5,2=10,3=253,4=254,5=255,6=256,7=257,8=258 then 10=? | [
"2",
"255",
"345",
"445",
"235"
]
| 1=5,2=10,3=253,4=254,5=255,6=256,7=257,8=258 then 10=?
10=2
check the first eqn.
ANSWER:A
The answer is: A | A |
mathematics | A part of certain sum of money is invested at 6% per annum and the rest at 15% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? | [
"4:6",
"4:9",
"4:3",
"5:2",
"4:2"
]
| 15:6
= 5:2
Answer: D
The answer is: D | D |
mathematics | A man took some money for borrowed, for 3 years the total will be Rs.5000 and 5 years it will be Rs.6000/-. Then how much amount he borrowed? | [
"s.2000/-",
"s.2500/-",
"s.2770/-",
"s.2800/-",
"s.3500/-"
]
| 3 years --------> Rs.5000/-
5 years --------> Rs.6000/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.5000/- - Rs.1500/- = Rs.3500/-
P = Rs.3500/-
E
The answer is: E | E |
mathematics | If x+y=20, x-y=36, for integers of x and y, x=? | [
"20",
"25",
"28",
"20",
"42"
]
| x+y = 20
x-y = 36
2x =56
x = 28
Answer is C
The answer is: C | C |
mathematics | In a 300 m race A beats B by 22.5 m or 6 seconds. B's time over the course is: | [
"86 sec",
"80 sec",
"76 sec",
"96 sec",
"None of these"
]
| runs 45/2m in 6 sec.
B covers 300 m in 6 x 2/45 x 300sec = 80 sec.
ANSWER:B
The answer is: B | B |
mathematics | 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.630 find the share of A. | [
"240",
"88",
"77",
"266",
"121"
]
| (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240.
Answer: A
The answer is: A | A |
mathematics | A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent? | [
"65%",
"67%",
"45%",
"78%",
"25%"
]
| E
800 --- 200
100 --- ? => 25%
The answer is: E | E |
mathematics | We made a down payment of $100 and borrowed the balance on a new piano which cost $1000. The balance with interest was paid in 23 monthly payments of $40 each and a final payment of $70. The amount of interest paid was what percent of the amount borrowed? | [
"6%",
"7%",
"8%",
"9%",
"10%"
]
| We borrowed $900.
To pay back this loan, we paid 23*$40 + $70=$990.
The interest was $990-$900=$90.
The percentage was $90/$900=0.1=10%.
The answer is E.
The answer is: E | E |
mathematics | If c≠d and c·d≠0, which of the following may be true? | [
"c.d =0",
"c-d=0",
"c+d=2",
"(c+d)(c-d)=0",
"c−d=d−c"
]
| except D all conditions are not as per question
D
The answer is: D | D |
mathematics | Find the area of a parallelogram with base 30 cm and height 12 cm? | [
"290 cm2",
"360 cm2",
"270 cm2",
"280 cm2",
"260 cm2"
]
| Area of a parallelogram = base * height = 30 * 12
= 360 cm2
Answer:B
The answer is: B | B |
mathematics | If one-third of one-fourth of a number is 15, then three-tenth of that number is | [
"35",
"36",
"45",
"54",
"57"
]
| Let the number be x. then 1/3 of ¼ of x=15
X=15x12=180
The required number=(3/10)*180=54
ANSWER D 54
The answer is: D | D |
mathematics | Let y = 2m + x^2 and m = 5x + 2. If m^2 =49, then which of the following can be a value of 2y + 3m? | [
"48",
"56",
"61",
"51",
"71"
]
| m^2 = 49 => m=7
7= 5x+2 => x=1
y= 2*7+1^2 = 15
2y+3m = 2*15+3*7 = 51
Answer : D
The answer is: D | D |
mathematics | Of the 90 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool? | [
"10",
"15",
"20",
"25",
"35"
]
| Neither Car nor Garage
= Total - Garage - (Swim - Common)
= 90 - 50 - (40-35) = 90-55 = 35
Answer E
The answer is: E | E |
mathematics | Divide $1000 among A,B in the ratio 1:4. How many $ that B get? | [
"$500",
"$800",
"$1000",
"$200",
"$750"
]
| Sum of ratio terms = 1+4 = 5
A = 1000*4/5 = $800
Answer is B
The answer is: B | B |
mathematics | (51+52+53+………+100) is equal to: | [
"2525",
"2975",
"3225",
"3775",
"3875"
]
| (51+52+53+………+100) = (1+2+3+…….+100)- (1+2+3+4+……+50)
= (100*101)/2 - (50*51)/2
= (5050-1275)= 3775.
ANSWER:D
The answer is: D | D |
mathematics | The average (arithmetic mean) of all scores on a certain algebra test was 90. If the average of the 8 male students’ grades was 82, and the average of the female students’ grades was 92, how many female students took the test? | [
"8",
"9",
"10",
"21",
"32"
]
| Total Marks of male = M
Total Marks of female = F
Number of males = 8
Number of females = f
Given: (M+F)/(8+f) = 90 -------------1
Also given, M/8 = 82 Thus M = 656 ---------2
Also, F/f = 92 thus F = 92 F - --------3
Put 2 and 3 in 1: we get
(656+92f)/(8+f) = 90
solving this we get f = 32
Ans: E
The answer is: E | E |
mathematics | The mean of set A does not exceed mean of any subset of set A. Which of the following must be true about set A?
I. Set A contains only one element
II. All elements in set A are equal
III. The median of set A equals the mean of set A | [
"of the three qualities is necessary",
"II only",
"III only",
"II and III only",
"I, II, and III"
]
| The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. A = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
The answer is: D | D |
mathematics | Let C represent a set of four distinct prime numbers. If the sum of the numbers in C is even and x is a member of C, then what is the least possible value that x can be? | [
"1",
"2",
"3",
"5",
"7"
]
| We are told that C is a set of four distinct prime numbers, and the sum of the numbers in C is even. Since the question involves odds, evens and the smallest possible prime, you should immediately think of 2, the smallest prime number and the only even prime number.
If 2 were a member of the set, then we would have one even number and three odd numbers. Since such sum would always be odd, 2 cannot be a member of the set. Thus, all the members of C must be odd to yield an even sum.
Since all the members of the set must be odd prime numbers, the answer is the smallest odd prime number, which is 3.
The correct answer is choice (C).
Note:1 is not a prime number.
The answer is: C | C |
mathematics | A train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is? | [
"238",
"180",
"988",
"177",
"171"
]
| Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 120)/25 = x/15 => x = 180 m.
Answer: B
The answer is: B | B |
mathematics | Raj invested an amount of Rs.17400 for two years. Find the rate of compound interest that will fetch him an amount of Rs.1783.50 at the end of two years? | [
"4",
"3",
"2",
"5",
"6"
]
| Let the rate of interest be R% p.a.
17400[1 + R/100]2 = 17400 + 1783.50
[1 + R/100]2 = (17400 + 1783.50)/17400
= 1 + 1025/10000 = 1 + 41/400
= 441/400 = [21/20]2
[1 + R/100] = 21/20
R/100 = 1/20
Therefore R = 5
Answer: D
The answer is: D | D |
mathematics | A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? | [
"65 Kmph",
"70 Kmph",
"72 Kmph",
"75 Kmph",
"78 Kmph"
]
| Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
ANSWER:C
The answer is: C | C |
mathematics | A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible? | [
"12",
"15",
"18",
"24",
"27"
]
| XYZYX
X can be 1, 2, or 3, thus 3 options.
Y can be 1, 2, or 3, thus 3 options.
Z can be 1, 2, or 3, thus 3 options.
Total 3^3=27.
Answer: E.
The answer is: E | E |
mathematics | For 1rs 4p interest
wat will be for 2000rs? | [
"45Rs",
"80Rs",
"40Rs",
"30Rs",
"48Rs"
]
| For 1rs , 4p interest
for 2000rs, x
x= 2000/1 * 4p ==> 8000 paise
To express in rs, 8000/100 = 80rs
ANSWER:B
The answer is: B | B |
mathematics | If s, t, and u are distinct positive prime numbers, then (s^3)(t)(u) has how many different positive factors greater than 1? | [
"a. 8",
"b. 9",
"c. 12",
"d. 7",
"e. 27"
]
| Let Number is (s^3)(t)(u) = (1^3)(5)(6) = 30
We can write 30 as product of two numbers in following ways
1*30
2*15
3*10
5*6
4 cases = 4*2 i.e. 8 factors (including 1)
Factors greater than 1 = 7
Answer: Option D
The answer is: D | D |
mathematics | A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? | [
"Rs.3948",
"Rs.3929",
"Rs.3927",
"Rs.3900",
"Rs.3928"
]
| Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
The answer is: D | D |
mathematics | Mr. LISA invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $200,000. In one year, Fund X paid 41% and Fund Y paid 14%. The interest earned in Fund Y was exactly $200 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X? | [
"60,545.56",
"570,545.56",
"50,545.45",
"80,545.23",
"90,545.78"
]
| X+Y=200,000
0.14Y=0.41A+200
Take away decimals first: 14Y+41X+20,000
Isolate first equation to solve for X (your goal): Y=200,000-Y
Plug in for B:
14(200,000-X)=41X+20,000
2,800,000-14X=41X+20,000
2,780,000=55X
2,780,000/55=X
X=50,545.45=Answer Choice C
The answer is: C | C |
mathematics | Meg and Bob are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob? | [
"24",
"30",
"60",
"90",
"120"
]
| Let me redeem myself:
JXXXX => Bob can be in any X...Total 4! = 24
XJXXX => Bob can be in the last 3 Xs...Total 3! = 6. However, since the first person can change too and it cannot be Bob, it can only be 3 other people. So Total = 6*3 = 18
XXJBX => 3! = 6 total
XXJXB => 3! = 6 total
So this yields total of 12
XXXJB => 3! = 6
Ans = 24+18+12+6 = 60
answer is C
The answer is: C | C |
mathematics | A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 4120 a year. What is his average monthly income? | [
"2000",
"2010",
"2100",
"2200",
"2300"
]
| Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 4120 = Rs. 24120
So, Average monthly income = 24120/12 = Rs. 2010
B
The answer is: B | B |
mathematics | What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ? | [
"Rs. 108",
"Rs. 120",
"Rs. 102",
"Rs. 106",
"None of these"
]
| Explanation :
Present Worth, PW = F - TD = 540 - 90 = Rs. 450
Simple Interest on the Present Worth = True Discount
Hence Simple Interest on 450 = 90 ------(Equation 1)
Simple Interest on the face value = Bankers Discount
=> Simple Interest on 540 = Bankers Discount
From Equation 1, Simple Interest on 450 = 90
Hence, Simple Interest on 540 = 90/450×540=540/5 = Rs. 108
=> Bankers Discount = Rs. 108 Answer : Option A
The answer is: A | A |
mathematics | You collect coins. Suppose you start out with 11. Since his mother makes coins, Miguel decides to double your coins. Since you're nice, you give Mary 12 coins. How many coins do you have at the end? | [
"9",
"10",
"11",
"12",
"13"
]
| Solution
Start with 11 coins.
Miguel doubles the number of coins you have: 11 × 2 = 22 coins.
Mary takes 12 coins from you: 22 - 12 = 10 coins.
So you have 10 at the end.
Correct answer: B
The answer is: B | B |
mathematics | The ratio of Laxmi's age to the age of her mother is 3:11. The difference of their ages is 24 years. The ratio of their ages after 3 years will be? | [
"1 : 9",
"1 : 3",
"1 : 2",
"1 : 1",
"3 : 3"
]
| Suppose age of Laxmi is x years.
The difference of their ages
\inline \therefore Ratio of their ages after 3 years = =
= 12 : 36 = 1 : 3
Answer:B
The answer is: B | B |
mathematics | A group of three women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers? | [
"7! – 2!3!2!",
"6! – 4!3!",
"7! – 5!3!",
"7 × 2!3!2!",
"2!3!2!"
]
| 6 people can sit in 6! different ways. But because 3 men cannot sit together, we take them as a unit.
This unit of men, among themselves can sit in 3! ways.
Hence, 6! - 3!.
This unit of men along with3 women can sit in 4! different ways which also needs to be eliminated.
Hence 6! - 4!3!
B
The answer is: B | B |
mathematics | If a and b are positive integers, and a=3b+12, the greatest common divisor of a and b CANNOT be | [
"1",
"3",
"2",
"5",
"4"
]
| If b is 1, 2, 3, or 4, then GCD of a and b is 1, 2, 3, and 4 respectively. So, by POE the answer must be D.
Still: if b is a multiple of 5, then a is 12 greater than a multiple of 5, so not a multiple of 5, so both of them cannot be divisive by 5.
Answer: D.
The answer is: D | D |
mathematics | A train 125 m long pass a telegraph pole in 5 seconds. Find the speed of the train | [
"90 km/hr",
"68.4 km/hr",
"72 km/hr",
"79.2 km/hr",
"None"
]
| Sol.
Speed = [125/5] m/sec = [25 * 18/5] km/hr = 90 km/hr.
Answer A
The answer is: A | A |
mathematics | Amber works 8 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay? | [
"8d",
"20d",
"10md/6",
"20d/m",
"20md"
]
| ANSWER: A The passage states that she works 8 days a month at d dollars per day, so 8 d is her monthly pay
The answer is: A | A |
mathematics | Nitin ranks 23th in a class of 60 students. What is rank from the last ? | [
"33",
"38",
"32",
"28",
"19"
]
| Explanation:
Number students behind the nitin in rank = (60 - 23) = 37
Nitin is 38nd from the last
Answer: B) 38
The answer is: B | B |
mathematics | A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green? | [
"23/35",
"29/35",
"47/70",
"43/70",
"None of these"
]
| Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
ANSWER:A
The answer is: A | A |
mathematics | A and B can do a piece of work in 40 days and 40 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? | [
"30days",
"35days",
"40days",
"45days",
"50days"
]
| Explanation:
(A+B)’s 10 days work = 10[1/40+1/40]=10[1+1/40]= 1/2
A complete remaining work in 1/2*40 = 20
Total work = 10+20 = 30days
Answer: Option A
The answer is: A | A |
mathematics | What percent of 60 is 90? | [
"133 1⁄3",
"150",
"60",
"33 1⁄3",
"25"
]
| % of 60 is 90?
= 90/60 = 3/2 = 150%
Thus B is the correct answer.
The answer is: B | B |
mathematics | Of the three-digit integers greater than 400, how many have two digits that are equal to each other and the remaining digit different from the other two? | [
"90",
"82",
"80",
"45",
"36"
]
| To satify the given condition,
required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,
number greater than 700;
total numbers = 1*10*10 = 100
numbers with all digits different = 1*9*8 = 72
numbers when all three digits are same (777) = 1
req. = 100- 72 - 1 = 27
considering the numbers between 700999 = 27*3=37
Answer is 36('cause 700 can't be included)
Answer (E).
The answer is: E | E |
mathematics | A train covers a distance of 12 km in 10 min. If it takes 9 sec to pass a telegraph post, then the length of the train is? | [
"177 m",
"189 m",
"120 m",
"178 m",
"180 m"
]
| Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 9
= 180 m.
Answer: E
The answer is: E | E |
mathematics | Compound interest of Rs.1000 at 10% per annum for 1 1/2years will be (interest compounded half yearly). | [
"Rs.473",
"Rs.374",
"Rs.495",
"Rs.157",
"None of the above"
]
| 10% interest per annum will be 5% interest half yearly for 3 terms( 1 1/2 years)
So compound interest=3000[1+(5/100)]^3 - 1000=1000[(21/20)^3 -1]
=1000(9261-8000)/8000
=1*1261/8
=157
ANSWER:D
The answer is: D | D |
mathematics | If a - b = 3, a^2 + b^2 = 29 ,find the value of ab. | [
"10",
"12",
"15",
"18",
"19"
]
| Explanation:
2ab = (a^2 + b^2) - (a - b)^2 = 29 - 9 = 20 => ab = 10..
Answer: A
The answer is: A | A |
mathematics | A man can row downstream at 26 kmph and upstream at 22 kmph. Find the speed of the man in still water and the speed of stream respectively? | [
"24, 2",
"12, 6",
"15, 3",
"14, 4",
"None of these"
]
| Explanation:
Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 26 --- (1)
and x - y = 22 --- (2)
From (1) & (2) 2x = 48 => x = 24, y = 2.
Answer: Option A
The answer is: A | A |
mathematics | Tommy has a lot of Lego blocks, but only green and red blocks. There are four times as many green blocks as there are red blocks. If Tommy has Y Lego blocks, how many red blocks are there, in terms of Y. | [
"3*Y",
"Y/3",
"Y/5",
"Y/4",
"Y/6"
]
| Since Y equals the number of blocks, then Y = Green + Red
Since there are four times green blocks as red blocks, then Green = 4*Red
Thus Y = 4*Red + Red, which simplifies to Y=5*Red
Therefore the Red = Y/5
Answer: C
The answer is: C | C |
mathematics | A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? | [
"Rs.600",
"Rs.500",
"Rs.250",
"Rs.700",
"Rs.800"
]
| Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
ANSWER:A
The answer is: A | A |
mathematics | The speed at which a man can row a boat in still water is 6.5 kmph. If he rows downstream, where the speed of current is 2.5 kmph, what time will he take to cover 90 metres? | [
"90 seconds",
"36seconds",
"26 seconds",
"18 seconds",
"6.5 seconds"
]
| Speed of the boat downstream = 6.5 + 2.5
= 9 kmph
= 9 * 5/18 = 2.5 m/s
Hence time taken to cover 90m =90/2.5
= 36 seconds.
Answer:B
The answer is: B | B |
mathematics | Departments A, B, and C have 4 employees each, and department D has 20 employees. Departments A, B, C, and D have no employees in common. A task force is to be formed by selecting 1 employee from each of departments A, B, and C and 2 employees from department D. How many different task forces are possible? | [
"12,610",
"40,000",
"100,000",
"190,000",
"400,000"
]
| 4c1 * 4c1* 4c1*20c2 = 10*10*10*190=12,610. Hence A is the correct answer.
The answer is: A | A |
mathematics | A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3? | [
"1/3",
"2/3",
"3/7",
"3/11",
"None"
]
| |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
C
The answer is: C | C |
mathematics | Let's say in a lottery Samuel have a 4% chance of winning the jackpot.
All lined up and 1st four people on the line lose. Samuel is 5th in the row.
What's the chance of Samuel winning now? | [
"2%",
"3%",
"4%",
"5%",
"6%"
]
| Solution:
4%
Explanation:
The winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.
Answer C
The answer is: C | C |
mathematics | The train travels at an average speed of 25km/h, to the top of the hill where the midpoint of the trip is. Going down hill, train travels at an average speed of 5km/h. Which of the following is the closest approximation of train's average speed, in kilometers per hour, for the round trip? | [
"8.5",
"8.3",
"2.6",
"4.2",
"6.5"
]
| Since we're not given a distance to work with, we can TEST any distance that we like. Here, since the speeds are 25 km/hour and 5 km/hour, using a multiple of both 25 and 5 would make the math easiest.
Let's set the Distance up the hill at 50 km.
So, going uphill, we have....
D = (R)(T)
50 = (25)(T)
50/25 = 2 = T
2 hours to go uphill
Going downhill, we have....
D = (R)(T)
50 = (5)(T)
50/5 = 10 = T
10 hours to go downhill
Total Distance = 100 km
Total Time = 10+2 = 12 hours
Average Speed = 100/12 = 8.3 km/hour
B
The answer is: B | B |
mathematics | A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? | [
"32 kmph",
"34 kmph",
"30 kmph",
"45 kmph",
"65 kmph"
]
| US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
The answer is: C | C |
mathematics | A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform? | [
"200",
"240",
"250",
"260",
"270"
]
| Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: Option B
The answer is: B | B |
mathematics | A and B complete a job in 6 days. A alone can do the job in 15 days. If B works alone, how many days will it take to complete the job? | [
"8",
"10",
"12",
"14",
"16"
]
| The rate of A and B is 1/6
A's rate is 1/15
B's rate is 1/6 - 1/15 = 1/10
B can complete the job in 10 days.
The answer is B.
The answer is: B | B |
mathematics | The average score of a cricketer for seven matches is 56 runs. If the average for first four matches is 46, then average for last three matches is | [
"33.25",
"32.25",
"65",
"67",
"69"
]
| Explanation:
=(56×7)−(46×4)/3
=(392−184)/3=69
Answer: Option E
The answer is: E | E |
mathematics | In a T.V. factory, an average of 60TVs are produced per day for the fist 25days of the months. A few workers fellill for the next five daysreducing the daily avg for the month to58 sets/day . The average production per day for day last 5days is ? | [
"35",
"39",
"48",
"50",
"52"
]
| Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
The answer is: C | C |
mathematics | If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $76, how much does one shirt cost? | [
"$10",
"$12",
"$13.20",
"$15",
"$18"
]
| 3J + 2S = 69
2J + 3S = 76
----------------
5J + 5S = 145 ----(divide by 5)---> J + S = 29
3J + 2S = J + 2(J + S) = J + 58 = 69 ---> J = 11
3*11 + 2S = 69
33 + 2S = 69
2S = 36
S = 18
Answer: E
The answer is: E | E |
mathematics | The average age of 4 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is | [
"22",
"30",
"99",
"26",
"27"
]
| total age increased = (8 * 2) years = 8 years.
Sum of ages of two new men = (21 + 23 + 8) years = 52 years
Average age of two new men = (52/2) years = 26 years.
Answer: D
The answer is: D | D |
mathematics | A bag contains 7 white balls, 5 black balls, and 4 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? | [
"1/2",
"1/4",
"3/8",
"5/12",
"2/5"
]
| The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 4/16 = 1/4.
The answer is B.
The answer is: B | B |
mathematics | If a man buys 10 lollipops for $90 and sold them for $2 dollars determine his loss. | [
"50",
"60",
"70",
"80",
"90"
]
| Cost of 10 lollipops = $90
Sold each lollipop for $2
So he sold 10 lollipops for $(10 × 2) = $20
Loss = $(90 – 20) = $70
answer :C
Therefore, loss = $ 70.
The answer is: C | C |
mathematics | If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) = | [
"3^(a + 1)",
"2^(a + 1)",
"2a",
"2a^(a + 1)",
"63(2^a)"
]
| If a is a positive integer, then 2^a + 2^(a + 1)+ 2^(a + 2)+ 2^(a + 3)+ 2^(a + 4)+ 2^(a + 5) =
2^a(1+2+4+8+16+32)
2^a(63)
E. 63(2^a)
The answer is: E | E |
mathematics | How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together. | [
"17280",
"4320",
"720",
"80",
"None of thsee"
]
| Explanation:
word SIGNATURE contains total 9 letters.
There are four vowels in this word, I, A, U and E
Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now
So total letter are 6.
6 letters can be arranged in 6! ways = 720 ways
Vowels can be arranged in themselves in 4! ways = 24 ways
Required number of ways = 720*24 = 17280
Option A
The answer is: A | A |
mathematics | When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder Q when N is divided by 30? | [
"(a) 4",
"(b) 7",
"(c) 11",
"(d) 13",
"(e) 17"
]
| N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder Q when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
The answer is: C | C |
mathematics | A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph? | [
"28",
"27",
"29",
"24",
"20"
]
| Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40
= 9/2 => x
= 20 km.
Answer: E
The answer is: E | E |
mathematics | k, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ? | [
"Rs. 1640",
"Rs. 2500",
"Rs. 2160",
"Rs. 3000",
"None of these"
]
| Explanation:
=> 60x5 : 36x6 : 75x3
=> 100 : 72 : 75
=> 72/247 x 7410 = Rs. 2160
ANSWER IS C
The answer is: C | C |
mathematics | A tradesman by means of his false balance defrauds to the extent of 40%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? | [
"80%",
"96%",
"92%",
"84%",
"86%"
]
| g% = 40 + 40 + (40*40)/100
= 96%
ANSWER:B
The answer is: B | B |
mathematics | If x and y are integers and 2x–y= 11, then 4x+ y CANNOT be | [
"–5",
"1",
"13",
"17",
"55"
]
| 2x-y=11
2x=11+y
4x=22+2y
now we need to check the value of 4x+4 => 22+2y+y=22+3y
hence 22+3y=value(in the options)
so y=value-22/3
so checking the options only D is unfit
ANSWER:D
The answer is: D | D |
mathematics | For any real number x, the operatoris defined as:
(x) = x(3 − x)
If p + 1 =(p + 1), then p = | [
"−3",
"0",
"1",
"2",
"3"
]
| (x) = x(1 − x)
(p + 1) = (p + 1)(3 - p - 1) =(2 -p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (2-p)(p+1) = (p + 1)
Or (p + 1) + (p-2)(p+1) = 0
(p + 1)(p-2) = 0
p = -1,p=2
Option D
The answer is: D | D |
mathematics | For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 171? | [
"2820",
"3440",
"4860",
"5560",
"6720"
]
| 100 + 102 + ... + 170 =
100*36 + (2+4+...+70) =
100*36 + 2*(1+2+...+35) =
100*36 + 2(35)(36)/2 =
100*36 + 35*36 = 135(36) = 4860
The answer is C.
The answer is: C | C |
mathematics | A boat has a speed of 14kmph in standing water. The stream has a speed of 1.2kmph. What time does the boat take to go to a distance of 4864 km and come back? (hours) | [
"700",
"378",
"2696",
"1207",
"1712"
]
| Explanation:
A boat travels at the speed of 14 km/hr in still water.
=> Speed of stream = 1.2 kmph
=> Speed of boat downstream becomes 14 + 1.2 = 15.2 kmph
=> Speed of boat upstream becomes 14 - 1.2 = 12.8 kmph
Total time taken in the journey = Journey downstream + Journey upstream
Therefore, 4864(1/12.8 + 1/15.2) = 700 hours
ANSWER: A
The answer is: A | A |
mathematics | Mike works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 500 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 62,500. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.? | [
"13000",
"12500",
"13500",
"14000",
"15000"
]
| let the rate be x, then population of the bacteria after each hour can be given as 500,500x, 500(x^2), 500(x^3)
now population at 4pm =62,500
thus we have 500(x^3) = 62,500 =125
thus x=5
therefore population at 3pm = 500(25) = 12500
Answer : B
The answer is: B | B |
mathematics | A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 25 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)] | [
"1/4",
"7/12",
"2/3",
"7/8",
"9/7"
]
| Let' take the Number of geese to be 100.
Male = 30. Female = 70.
Now the second part of the Q, Let's take the Number migrated to be 20.
So we have 20 geese that migrated and out of that 25% are male i.e 25/100 *20 = 5 Geese (Males)
And now we know out of the total 20 geese , 5 are male , then 15 have to be female.
Now the ratio part , Male Geese Ratios = 5/30 = 1/6. - A
Female Geese Ratios =15/70=3/14 - B
Cross Multiply Equations A and B and you get =9/7 .
Ans E
The answer is: E | E |
mathematics | A focus group is currently made up of x men and y women. If 3 men and 7 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a man is selected? | [
"x/(x + 7)",
"x/(x + y)",
"(y + 3)/(x + y + 7)",
"(y + 4)/(x + y + 10)",
"(x + 3)/(x + y + 10)"
]
| x men
y women
x+3+y+7 is the total
=x+y+10
x+3 is the number of men
so (x + 3)/(x + y + 10)
E. (x + 3)/(x + y + 10)
The answer is: E | E |
mathematics | Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 10 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X? | [
"34",
"35",
"36",
"37 1/25",
"40"
]
| In 8 kilograms of solution Y there are 0.3*10=3 kilograms of solution X;
After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*2=0.6 kilograms of solution X are added, so in the new solution of 8 kilograms there are 3+0.6=3.6 kilograms of solution X, which is 3.6/10*100=36% of this new solution.
Answer: C.
The answer is: C | C |
mathematics | If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 930, C will receive | [
"233",
"180",
"900",
"287",
"271"
]
| Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (930 * 6/31) = Rs, 180.
Answer: B) Rs.180
The answer is: B | B |
mathematics | The cost of the paint is rs.20 per kg. if 1kg of paint covers 15 sq.ft, how much will it cost to paint outside of a cube having 5 feet each side | [
"Rs.200",
"Rs.672",
"Rs.546",
"Rs.876",
"None of these"
]
| Explanation:
surface area of a cube= 6 x 5^2 = 150 sq.ft
quantity of paint required=(150/15)=10 kg
cost of painting= 20 x 10 = Rs.200
Answer: A
The answer is: A | A |
mathematics | Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is | [
"6 days",
"7 days",
"8 days",
"9 days",
"11 days"
]
| If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
C
The answer is: C | C |
mathematics | 33
a3
+4b
___
88
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab? | [
"12",
"10",
"13",
"24",
"34"
]
| 3+3+b=8
b=2
3+a+4=8
a=1
ab=12
ans=A
The answer is: A | A |
mathematics | If i is a positive integer and i^2 is divisible by 12, then the largest positive integer that must divide i ^3 is | [
"2^3",
"2^6",
"3^3",
"6^3",
"12^2"
]
| Since i is an integer so i cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making i^2 as a multiple of 12))
i^2 is divisible by 12 (12 = 2*2*3), So, i should have at least one 2 and one 3 so that i^2 has a 2^2 and two 3
So, i will have a 2 and a 3. Or i will be a multiple of 6
So, largest possible integer than should divide i^3 is 6^3
So, Answer will be D
The answer is: D | D |
mathematics | There is a 5% chance that Tigers will not win at all during the whole season. There is a 5% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Tigers will win and Federer will play during the season? | [
"55%",
"60%",
"70%",
"72%",
"95%"
]
| There is a 5% chance that Tigers will not win at all during the whole season
We can infer that there is 95% chance Tigers will win .
Similarly There is a 5% chance that Federer will not play at all in the whole season
We can also infer that there is 95% chance that Federer will play.
Answer E
The answer is: E | E |
mathematics | A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 21 hrs and a machine of type S does the same job in 42 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used? | [
"6",
"7",
"8",
"9",
"10"
]
| Type R completes 1/21 of the job each hour.
Type S completes 1/42 of the job each hour.
Together R and S complete 1/21 +1/42 = 1/14 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/14) = 1 job completed
n = 7
The answer is B.
The answer is: B | B |
mathematics | The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 10. What is the radius of circle O? | [
"–2/pi",
"2",
"3",
"4",
"5"
]
| pi*r^2 + 2r -2*pi*r = 10
Simplifying the equation: pi*r(r-2)+2r=10
Without much algebraic: We can Test the answers quickly, then 5 is the only possible answer that will eliminate pi from equation.
Answer is E
The answer is: E | E |
mathematics | Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks? | [
"1/3",
"1/5",
"1/6",
"1/7",
"2/5"
]
| Total number of ways to go home, considering that the order order matters =
Options: SSSEEE
Slots : ------
total permutations of 6 options in 6 slots: 6P6 = 6! = 6*5*4*3*2
Total ways to select "South" in the first 2 positions and anything else in the subsequent 4 positions =
Options: SS ????
Slots: -- ----
Permutations of 3 "S" in 2 slots AND Permutations of 4 Choices in 4 slots =
3P2 * 4P4 = 3! * 4! = 3*2*4*3*2
The probability is therefore:
3P2 * 4P4 = 6P6
3*2*4*3*2= 1/5
ANSWER:B
The answer is: B | B |
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