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mathematics | How many 4-letter word with or without meaning can be formed out
of the letters of the word 'LOGARITHMS' if repetition of letters is
not allowed | [
"2000",
"1000",
"5040",
"5000",
"500"
] | 'LOGARITHMS' contains 10 different letters
Required number of words
= Number of arrangements of 100 letters taking
4 at a time
= 10P4
= 10 * 9 * 8 * 7
= 5040
ANSWER C
The answer is: C | C |
mathematics | The largest number that exactly divides each number of the sequence
(15 - 1), (25 - 2), (35 - 3), ...., (n5 - n), ...... is | [
"1",
"15",
"30",
"120",
"None"
] | Sol.
Required number = (25 - 2)
= (32 - 2) = 30.
Answer C
The answer is: C | C |
mathematics | The cost of 3 kg of sugar is $90. What will the cost of 8 kg of sugar be? | [
"120",
"140",
"180",
"220",
"240"
] | 3 kg costs $90
1 kg costs $30
8 kg costs $240
The answer is E.
The answer is: E | E |
mathematics | (469 + 174)^2 - (469 - 174)^2 /(469 x 174)= ? | [
"643",
"2",
"295",
"4",
"185"
] | Given exp. =(a + b)^2 - (a - b)^2/ab
=4ab/ab
= 4 (where a = 469, b = 174.)
Answer is D.
The answer is: D | D |
mathematics | A reduction of 48% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen? | [
"2.6",
"8.6",
"7.6",
"3.6",
"1.6"
] | Explanation:
40*(48/100) = 19.2 --- 64
? --- 12 => Rs.3.6
Answer: D
The answer is: D | D |
mathematics | A side of an equilateral triangle is tripled. If the previous parameter is 3x, what is the length of one of the sides before it was tripled? | [
"4x",
"3x",
"1x",
"2x",
"6x"
] | If the parameter before it was tripled 3x, one of the sides must have been 3x/3. This reduces to 1x. Answer option C.
The answer is: C | C |
mathematics | Line R has the equation 3x + y = 7. Which of the following lines is perpendicular to Line R? | [
"y = 3x + 4",
"y = β3x β 6",
"y = (1/3)x β 1",
"y = (β1/3)x + 2",
"y = (β7/3)x β 5"
] | I first rewrote the equation in the standard y=mx+b form. Therefore, Line R as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line R? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
The answer is: C | C |
mathematics | John buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods. | [
"Rs. 6876.10",
"Rs. 4500",
"Rs. 4600",
"Rs. 3400",
"Rs. 7500"
] | Rebate = 6% of Rs. 6650 = Rs. 6 x 6650 = Rs. 399.
100
Sales tax = 10% of Rs. (6650 - 399) = Rs. 10 x 6251
= Rs. 625.10
100
Final amount = Rs. (6251 + 625.10) = Rs. 6876.10
correct answer - A
The answer is: A | A |
mathematics | Divide 5679 by 7 and find out remainder and quotient ? | [
"901, 5",
"811, 2",
"921, 7",
"805, 4",
"951, 20"
] | dividend = divisor * quotient + remainder ===> 5679 = 7 * 811 + 2 ===> remainder = 2 and quot = 811 Ans - B
The answer is: B | B |
mathematics | Bobby bought two shares of stock, which he sold for $96 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined Bobby had: | [
"A profit of $10",
"A profit of $8",
"A loss of $8",
"A loss of $10",
"Neither a profit nor a loss"
] | Cost of the first stock: 96/1.2=80, so profit from it 96-80=16
Cost of the second stock: 96/0.8=120, so loss from it 96-120=-24
Overall loss 16-24=-8
Answer: C.
The answer is: C | C |
mathematics | Jacob is 18years old. He is 2 times as old as his brother. How old will Jacob be when he is twice as old? | [
"36",
"38",
"33",
"32",
"38"
] | j=18;
j=2b;
b=18/2=9;
twice as old so b=9(now)+(9)=18;
jacob is 18+18=36
ANSWER:A
The answer is: A | A |
mathematics | There are 10 red balls, 10 blue balls, 15 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color? | [
"10",
"23",
"43",
"41",
"16"
] | The worst case scenario would be if we pick 9 red balls, 9 blue balls, 14 (?) balls and 8 black balls. In this case we'll have 11+9+14+8=40 balls and still won't have all the balls of one color. The next 41rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: D.
The answer is: D | D |
mathematics | If a positive integer n has 211 factors,then how many prime factors does n have? | [
"3",
"2",
"cannot be determined",
"4",
"1"
] | Let the factor be a^x*b^y.....
So (x+1)(y+1).....=211..
Now 211 is a prime number...
So only one variable x or y is 210 and the others are 0..
(210+1)(0+1)...
So the number becomes a^210..
Thus only ONE prime factor is there.
The answer is: E | E |
mathematics | After striking the floor, a rubber ball rebounds to 4/5th of the height from which it has fallen. Find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres. | [
"540 m",
"960 m",
"1080 m",
"1020 m",
"1120 m"
] | Solution: The first drop is 120 metres. After this the ball will rise by 96 metres and fall by 96 metres. This process will continue in the form of infinite GP with common ratio 0.8 and first term 96. The required answer is given by the formula:
a/(1-r)
Now,
[{120/(1/5)}+{96/(1/5)}]
= 1080 m.
Answer C
The answer is: C | C |
mathematics | A certain kind of fuel is 1515high octane and 4545regular octane. If high octane costs three times as much as regular octane, what fraction of the cost of the fuel is due to the high octane? | [
"1/5",
"2/3",
"3/7",
"3/5",
"4/5"
] | let x be the amount of fuel
high octane = x/5
regular = 4x/5
price of regular = y
price of high octante = 3y
cost of high octane in the fuel = 3y * x/5
total cost = 3y * x/5 + 4x/5 * y
% = cost of high octante / total cost
= 3/7
Answer is C
The answer is: C | C |
mathematics | A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey? | [
"76 kmph",
"24 kmph",
"99 kmph",
"55 kmph",
"44 kmph"
] | Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.Answer:B
The answer is: B | B |
mathematics | The area of a triangle is with base 4m and height 5m? | [
"88 m2",
"10 m2",
"66 m2",
"77 m2",
"31 m2"
] | 1/2 * 4 * 5 = 10 m2
Answer: B
The answer is: B | B |
mathematics | A train covers a distance of 12 km in 10 min. If it takes 15 sec to pass a telegraph post, then the length of the train is? | [
"250 m",
"300 m",
"120 m",
"200 m",
"166 m"
] | Speed = (12/10 * 60) km/hr
= (72 * 5/18) m/sec
= 20 m/sec.
Length of the train
= 20 * 15
= 300 m.
Answer:B
The answer is: B | B |
mathematics | A,B,C subscribe Rs.50,000 for a business.A subscribes Rs.4000 more than B and B Rs.5000 more than C.Out of a total profit of Rs.35,000,A receives : | [
"Rs.8400",
"Rs.11,900",
"Rs.13,600",
"Rs.14,700",
"None of these"
] | Solution
Let C = x.Then, B = x + 5000 and A = x + 5000 + 4000 - x + 9000.
So, x + x + 5000 + x + 9000 - 50000 3x - 36000 x =12,000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
β΄ Aβs share = Rs. (35000x21/50) = Rs. 14,700. Answer D
The answer is: D | D |
mathematics | Let q represent the integer length of a side of a triangle. If r represents the number of distinct values for q such that we can create a triangle with lengths q, 12, and 19, what is the value of r? | [
"15",
"22",
"23",
"25",
"31"
] | From the triangle inequality rule, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, the three inequalities are:
1. q + 12 > 19
2. 12 + 19 > q
3. q + 19 > 12
Equation 3 is true for any positive value of q.
From equation 1, q > 7
From equation 2, 31 > q
Then 31 > q > 7 so q can be any value from 8 to 30 inclusive.
The number of possible values is 23.
The answer is C.
The answer is: C | C |
mathematics | The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 231 the Other is | [
"330",
"300",
"270",
"250",
"350"
] | The other number
= L.C.M * H.C.F/given number
= 2310*30/231 = 300
Answer is B.
The answer is: B | B |
mathematics | In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 565. What is the sum of the last 5 integers in the sequence? | [
"585",
"580",
"575",
"590",
"565"
] | All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+565=590
D
The answer is: D | D |
mathematics | A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)? | [
"16",
"20",
"24",
"28",
"32"
] | The height:length ratio will be equal in both cases.
18 / 45 = x / 50
x = 20
The answer is B.
The answer is: B | B |
mathematics | In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of: | [
"Rs. 3100",
"Rs. 6240",
"Rs. 6500",
"Rs. 9600",
"Rs. 9000"
] | Explanation:
To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment = Rs. 96 /10 *650=Rs. 6240.
ANSWER IS B
The answer is: B | B |
mathematics | Jeremy bought 2Q steaks for P dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents? | [
"50RP/Q.",
"50QR/P.",
"25RQ/P.",
"25RP/Q.",
"RP/(4Q)."
] | Jeremy bought 2Q steaks for P dollars, so 1 steak = P/2Q
Jerome buys R steaks for a 50% discount: r* (P/4Q)
in cents the answer will be : r* (100 P/4Q)= 25 RP/ Q=D
The answer is: D | D |
mathematics | Let S be the set of all positive integers n such that n^2 is a multiple of both 24 and 108. Which of the following integers are divisors of every integer n in S ? | [
"12",
"24",
"120",
"72",
"182"
] | 4 = 2^3*3;
108 = 2^2*3^3.
The smallest perfect square (n^2) which is a multiple of both 24 = 2^3*3 and 108 = 2^2*3^3 is 2^4*3^4, thus the smallest n is 2^2*3^2 = 36. So, only 12 is a divisor of all integers in S.
Answer: A.
The answer is: A | A |
mathematics | Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is: | [
"Rs. 5400",
"Rs. 7200",
"Rs. 8400",
"Rs. 9600",
"None of these"
] | Explanation:
Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
ANSWER IS C
The answer is: C | C |
mathematics | Find the average of first 40 natural numbers. | [
"20.5",
"18",
"19.5",
"19",
"17"
] | Exp. Sum of first n natural numbers = n( n+1)/2
So, sum of first 40 natural numbers = 40*41/2 = 820
Required average =820/40 =20.5
Answer:A
The answer is: A | A |
mathematics | Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank? | [
"A16",
"G4",
"E4",
"E3",
"None"
] | Explanation: The letters decrease by 1; the numbers are multiplied by 2.
Answer: Option C
The answer is: C | C |
mathematics | A certain university will select 3 of 7 candidates eligible to fill a position in the mathematics department and 5 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? | [
"42232",
"42170",
"14008",
"16510",
"41160"
] | 7C3*8C5 = 35*56 = 41160
the answer is (E)
The answer is: E | E |
mathematics | Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 10 as remainder | [
"1235",
"1456",
"1567",
"1636",
"1635"
] | Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 10
5x = 1355
x = 271
Large number = 271+1365 = 1636
D
The answer is: D | D |
mathematics | What is the area of square field whose side of length 15 m? | [
"225 sq m",
"286 sq m",
"298 sq m",
"267 sq m",
"231 sq m"
] | 15 * 15
= 225 sq m
Answer:A
The answer is: A | A |
mathematics | 10 play kabadi, 25 play kho kho only, 5 play both gmaes. Then how many in total? | [
"30",
"35",
"38",
"40",
"45"
] | 10 play kabadi =>n(A)=10,
5 play both gmaes.=> n(AnB)=5
25 play kho kho only,=>n(B)=n(B only)+n(AnB)=25+5=30
Total => n(AUB)= n(A)+n(B)-n(AnB)
= 10+30-5
= 35
ANSWER:B
The answer is: B | B |
mathematics | If a book is sold at 7% profit instead of 7% loss, it would have brought Rs 14 more. Find out the cost price of the book | [
"75",
"100",
"60",
"70",
"80"
] | Let C.P. of the book be Rs. βXβ
Given, 1.07 X - 0.93X = 14
=> 0.14 X = 14 = 14/0.14 = Rs 100
ANSWER:B
The answer is: B | B |
mathematics | The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ? | [
"10,68",
"10,16",
"10,12",
"10,10",
"10,11"
] | Explanation:
Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
let the price of one book be Rs. x
Then, the price of other book = Rs. (x + 60% of x) = Rs. = Rs.
So,
The prices of the two books are Rs. 10 and Rs. 16
Answer: B
The answer is: B | B |
mathematics | How many 4 digit odd numbers do not use any digit more than once | [
"1720",
"2160",
"224",
"2460",
"None of these"
] | The Way i solved it is
A B C D ( thousand , hundreds, tens, units)
D can be 1 3 5 7 9 ( any of the 5 digits )
A can be anything except (D or 0) so 8 possibilities
C can be anything execpt A and B so 8 possibilities
B can be anything execpt ( A D C ) so 7 possibilities
total ways are 8 * 7 * 8 * 5 = 2240
Ans E
The answer is: E | E |
mathematics | Two trains start simultaneously from opposite ends of a 175-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 175-km trip in 4 hours. Train Y, travelling at a constant rate, completes the 175-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y? | [
"66",
"69",
"72",
"75",
"78"
] | If the two trains cover a total distance D, then Train X travels (3/7)*D while Train Y travels (4/7)*D. If the trains travel 175 km to the meeting point, then Train X travels (3/7)*175 = 75 km. The answer is D.
The answer is: D | D |
mathematics | If 0 < a< 1 < b, which of the following must be true? | [
"1 < 1/a< 1/b",
"1/a< 1 < 1/b",
"1/a< 1/b< 1",
"1/b< 1 < 1/a",
"1/b< 1/a< 1"
] | 0<a<1<b. Let a=1/2 and b=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
The answer is: D | D |
mathematics | In a group of cows and chickens, the number of legs was 20 more than twice the number of heads. The number of cows was: | [
"5",
"7",
"10",
"12",
"14"
] | Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 20 more than twice the number of heads.
Therefore, 2 Γ (x + y) + 20 = 4x + 2y.
or, 2x + 2y + 20 = 4x + 2y.
or, 2x + 20 = 4x [subtracting 2y from both sides].
or, 20 = 4x β 2x [subtracting 2x from both sides].
or, 20 = 2x.
or, x = 10 [dividing by 2 on both sides].
Therefore, the number of cows = 10.
Correct Answer:C)10
The answer is: C | C |
mathematics | There are 20 brown dogs, 10 white dogs, 15 black dogs.Totally how many dogs are there in all? | [
"45",
"15",
"25",
"5",
"30"
] | 20+10+15=45. Answer is A
The answer is: A | A |
mathematics | Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in? | [
"8",
"7",
"6",
"9",
"5"
] | 1/10 + 1/15 - 1/x = 1/18
x = 9
Answer:D
The answer is: D | D |
mathematics | In a kilometer race, A beats B by 51 meters or 11 seconds. What time does A take to complete the race? | [
"22",
"190",
"277",
"204",
"208"
] | Time taken by B run 1000 meters = (1000 * 11)/51 = 215 sec.
Time taken by A = 215 - 11 = 204 sec.Answer:D
The answer is: D | D |
mathematics | Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 4 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive? | [
"20%",
"17%",
"4.0%",
"3.3%",
"2.8%"
] | 20/6 =3.33
Answer : D
The answer is: D | D |
mathematics | What Approximate Values should comein place of the question mark (?) in each of the following equations ?
85% of 225 + 56% of 450 + 32.98 x 5.001 = ? | [
"600",
"625",
"608",
"605",
"610"
] | Explanation :
85x225/100+56x450/100+33x5 = 85 x 2.25 + 56 x 4.5 + 165 = 608
Answer : Option C
The answer is: C | C |
mathematics | A certain kind of necklace is made from 9 green, 6 white, and 3 orange beads. What is the maximum number of these necklaces that can be made from 45 beads of each color ? | [
"7",
"8",
"5",
"6",
"2"
] | Atleast 9 green breads are needed to make a necklace, so irrespective of the combinations of white and orange beads, the number of necklaces that can be formed will be
45/9 =5
Answer:- C
The answer is: C | C |
mathematics | Find the largest 4 digit number which isexactly divisible by 88? | [
"5678",
"7654",
"9944",
"9950",
"10000"
] | Largest 4 digit number is 9999
After doing 9999 Γ· 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
The answer is: C | C |
mathematics | Jerryβs average (arithmetic mean) score on the first 3 of 4 tests is 90. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? | [
"87",
"89",
"90",
"98",
"95"
] | Total score on 3 tests = 90*3 = 270
Jerry wants the average to be = 92
Hence total score on 4 tests should be = 92*4 = 368
Score required on the fourth test = 368 - 270 = 98
Option D
The answer is: D | D |
mathematics | If an amount of Rs 26000 is divided equally among
76 students, approximately how much amount will
each student get? | [
"Rs 206",
"Rs 400",
"Rs 420",
"Rs 218",
"None"
] | Amount received by each student = 26000/65 Γ’β°Λ Rs
400
Answer B
The answer is: B | B |
mathematics | Zack has 3 red fish, 5 yellow fish and 7 green fish. How many fish does he have in all? | [
"8",
"5",
"15",
"1",
"18"
] | 3+5+7=15. Answer is C
The answer is: C | C |
mathematics | How many 3 digit numbers that do not contain the digit 0 are there? | [
"100",
"200",
"512",
"648",
"729"
] | Applying combinations....9 * 9 * 9 = 729...
8 for first digit...cant be 0
9 and 9 for 2nd and 3rd....cant be 0
ANSWER: E
The answer is: E | E |
mathematics | A man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour. The woman stops to wait for the man 3 minutes after passing him, while the man continues to walk at his constant rate. How many minutes must the woman wait until the man catches up? | [
"1",
"2",
"3",
"4",
"5"
] | When the woman passes the man, they are aligned (m and w). They are moving in the same direction. After 5 minutes, the woman (W) will be ahead the man (M):
m------M---------------W
w
In the 5 minutes, after passing the man, the woman walks the distance mW = wW, which is 3*15/60 =15/20 miles and the man walks the distance mM, which is 3*9/60 = 9/20 mile.
The difference of 15/20 - 9/20 =3/10 miles (MW) will be covered by the man in (3/10)/9 = 1/30 of an hour, which is 2 minutes.
Answer B.
The answer is: B | B |
mathematics | (132)^7 Γ (132)^? = (132)^11.5. | [
"4.5",
"3",
"4",
"3.5",
"8.5"
] | (132)^7 Γ (132)^x = (132)^11.5
=> 7 + x = 11.5
=> x = 11.5 - 7 = 4.5
Answer is A
The answer is: A | A |
mathematics | Danny obtained 76, 65, 82, 67 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? | [
"A)87",
"B)99",
"C)68",
"D)82",
"E)73"
] | Average = (76 + 65 + 82 + 67 + 75)/5
= 365/5
= 73.
Answer:E
The answer is: E | E |
mathematics | A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, and 4 at all. If repeated digits are allowed, what is the probability that it has at least one even digit? | [
"145/401",
"845/901",
"1145/1401",
"2145/2401",
"3145/3401"
] | P(no even digits) = 4/7*4/7*4/7*4/7 = 256/2401
P(at least one even digit) = 1 - 256/2401 = 2145/2401
The answer is D.
The answer is: D | D |
mathematics | In a school the number of girls is 30% the number of boys. Find the number of boys as a percentage of girls? | [
"112%",
"12%",
"333%",
"150%",
"16%"
] | It is given that in a school the number of girls is 30% the number of boys.
If boys=10
girls=3
We are asked for the number of boys as a percentage of girls
b/g=10/3=10 1/3=3.333=333%
Answer is C
The answer is: C | C |
mathematics | A car travels at a speed of 65 miles per hour. How far will it travel in 7 hours? | [
"125 miles",
"225 miles",
"455 miles",
"425 miles",
"525 miles"
] | During each hour, the car travels 65 miles. For 7 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 + 65 = 7 Γ 65 = 455 miles
correct answer is C) 455 miles
The answer is: C | C |
mathematics | John and Peter are among the seven players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter? | [
"5/11",
"8/15",
"9/20",
"10/21",
"11/24"
] | The total possible ways of selecting a 5-member team is 7C5 = 21
The possible ways which include John and Peter is 5C3 = 10
The probability of choosing both John and Peter is 10/21
The answer is D.
The answer is: D | D |
mathematics | In 1986 the book value of a certain car was 2/3 of the original price, and in 1988 its book value was 1/2 of the original purchase price. By what percent did the book value for this car decrease from 1986 to 1988? | [
"16 2/3 %",
"25 %",
"33 1/3 %",
"50%",
"75%"
] | 1986; 2/3
1988; 1/2
% decrease = change/original*100
2/3β1/2 / 2/3β100
1/6β3/2β100=14β100=25
Answer: "B"
The answer is: B | B |
mathematics | How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest? | [
"3.5 years",
"4 years",
"4.5 years",
"5 years",
"5.5 years"
] | Time = (100 x 81)/(450 x 4.5) = 4 years.
Answer: Option B
The answer is: B | B |
mathematics | A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? | [
"9:1",
"4:2",
"5:2",
"9:2",
"9:0"
] | Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Answer:A
The answer is: A | A |
mathematics | If x = 3 and y = -2, what is the value of 2(x-y)^2 - xy ? | [
"152",
"142",
"121",
"56",
"111"
] | x = 3 and y = -2
x-y = 3 - (-2) = 3+2 =5
x*y = 3 * -2 = -6
Now we apply it in the equation 2(x-y)^2 - xy =2 (5)^2-(-6)
==>2*25 +6 = 50+6 =56
Answer : D
The answer is: D | D |
mathematics | The perimeter of a semi circle is 198 cm then the radius is? | [
"22",
"28",
"98",
"38.5",
"13"
] | 36/7 r = 198
=> r
= 38.5
Answer: D
The answer is: D | D |
mathematics | On his first 5 tests, David received an average score of N points. If on his sixth test, he exceeds his previous average score by 36 points, what is his average score for his first 6 tests? | [
"N +12",
"N +6",
"N +3",
"N +8",
"N +18"
] | Total of 1st 5 tests= 5N
6th test score = N + 36
Total of all 6 tests = 6N + 36
Average = N +6
Answer : B
The answer is: B | B |
mathematics | There are 18 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season? | [
"1370",
"1530",
"1790",
"1950",
"2110"
] | The number of ways to choose two teams is 18C2 = 18*17/2 = 153
The total number of games in the season is 10*153 = 1530.
The answer is B.
The answer is: B | B |
mathematics | In the xy-coordinate system, what is the slope of the line that goes through the point (7, 3) and is equidistant from the two points P = (5, 5) and Q = (13, 7)? | [
"0.5",
"0.75",
"1.0",
"1.25",
"1.5"
] | First, get the middle coordinate between (5,5) and (13,7)...
x = 5 + (13-5)/2 = 9
y = 5 + (7-5)/2 = 6
Second, get the slope of (9,6) and (7,3). m = 6-3 / 9-7 = 3/2 = 1.5
Answer: E
The answer is: E | E |
mathematics | If k and t are integers and k^2 β t^2 is an odd integer, which of the following must be an even integer?
I. k + t + 2
II. k^2 + 2kt + t^2
III. k^2 + t^2 | [
"None",
"I only",
"II only",
"III only",
"I, II, and III"
] | k^2βt^2 is an odd integer means that either k is even and t is odd or k is odd and t is even.
Check all options:
I. k + t + 2 --> even+odd+even=odd or odd+even+even=odd. Discard;
II. k^2 + 2kt + t^2 --> even+even+odd=odd or odd+even+even=odd. Discard;
III. k^2 + t^2 --> even+odd=odd or odd+even=odd. Discard.
Answer: A.
The answer is: A | A |
mathematics | What is the least number of square tiles required to pave the floor of a room 10 m 17 cm long and 9m 9 cm broad? | [
"724",
"804",
"11413",
"844",
"None"
] | Solution
Length of largest tile = H.C.F. of 1017cm & 909cm = 9cm.
Area of each tile = (9 x 9)cm2
β΄ Required number of tiles = [1017x909/9x9]
= 11413.
Answer C
The answer is: C | C |
mathematics | A woman says, "If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum." The woman's age is? | [
"25 years",
"65 years",
"45 years",
"75 years",
"95 years"
] | Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.
Then, woman's age = (10X + y) years; husband's age = (10y + x) years.
Therefore (10y + x)- (10X + y) = (1/11) (10y + x + 10x + y)
(9y-9x) = (1/11)(11y + 11x) = (x + y) 10x = 8y x = (4/5)y
Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.
View Answer Discuss in Forum
Answer:C
The answer is: C | C |
mathematics | Sachin is younger than Rahul by 6 years. If the ratio of their ages is 7:9, find the age of Sachin | [
"24.58",
"14",
"15",
"24.9",
"24.1"
] | If Rahul age is x, then Sachin age is x-6,
so (x-6)/x = 7/9
=> 9x-42 = 7x
=> 2x = 42
=> x = 21
So Sachin age is 21 - 6 = 15
Answer: C
The answer is: C | C |
mathematics | Avinash is twice as fast as Bharat, and Bharat is one-third as fast as Chandra. If together they can complete a piece of work in 30 days, in how many days can Avinash, Bharat and Chandra do the work respectively? | [
"90,180,60",
"90,180,68",
"90,180,62",
"90,180,69",
"90,180,61"
] | Let Chandra do the work in 2x days.
Bharat can do it in 6x days and Avinash can do it in 3x days.
1/(2x) + 1/(6x) + 1/(3x) = 1/30 => (3 + 1 +2)/6x = 1/30 => x = 30
So, the time taken to complete the work by Avinash, Bharat, Chandra is 90, 180, 60 days respectively.
Answer:a
The answer is: A | A |
mathematics | As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 40%, what is the probability that Karen will be accepted to at least one project? | [
"317/500",
"141/250",
"98/125",
"67/100",
"23/50"
] | Since the probability of Karen's being accepted to each individual project is 40%, the probability of her not being accepted to each project is 60%. The probability that she will be accepted to none is, therefore, (3/5)*(3/5)*(3/5)=27/125.
P(Karen will be accepted to at least one project) = 1 - (27/125) = 98/125.
The answer is C.
The answer is: C | C |
mathematics | The profit earned by selling an article for 852 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit? | [
"960",
"975",
"1,200",
"920",
"None of these"
] | Let the profit or loss be x
and 852 β x = 448 + x or, x = 404β2 = 202
\ Cost price of the article = 852 β x = 448 + x = 650
\ SP of the article = 650 Γ 150β100 = 975
Answer B
The answer is: B | B |
mathematics | You have been given a physical balance and 7 weights of 43, 45, 30, 33, 28, 37 and 55 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 145 kgs. | [
"145",
"143",
"147",
"141",
"142"
] | 55 + 43 + 45 = 143
Answer: B
The answer is: B | B |
mathematics | 6 college friends go on vacation together during spring break. Their rental house costs $1250. If each friend pays the same amount and no one has bills smaller than $1, how much money do they pay for the rental? | [
"$1250",
"$1251",
"$1252",
"$1253",
"$1254"
] | In order to divide the sum in 6 parts, the amount must be divisible by 6.
Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
We need to make this number even in order for it to be divisible by 2.
Sum of digits of 1250 = 8 and 12 is divisible by both 3 and yields an even number.
Hence, we need to add 4 to this number for it to be divisible by 6
Correct Option: E
The answer is: E | E |
mathematics | When p is divided by 9, the remainder is 4. All of the following are possible values of p, except for which of the following? | [
"13",
"31",
"49",
"52",
"67"
] | If a number is divisible by 9, the sum of its digits must be divisible by 9. --> If a number leaves a remainder 4 when divided by 9 the sum of its digits must be 4.
52
Answer: D
The answer is: D | D |
mathematics | Jasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so.
If she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides? | [
"1",
"2",
"3",
"4",
"5"
] | 3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done.
The answer is: C | C |
mathematics | A set consists of 15 numbers, all are even or multiple of 5. If 8 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10? | [
"0",
"1",
"2",
"3",
"5"
] | {Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
15 = 8 + 10 - {Both} + 0;
{Both}=3(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: D.
The answer is: D | D |
mathematics | 20% of a number is more than 30% of 120 by 80. Find the number? | [
"520",
"560",
"580",
"620",
"610"
] | (20/100) * X β (30/100) * 120 = 80
1/5 X = 116
X = 580
Answer:C
The answer is: C | C |
mathematics | The positive number a is q percent greater than the positive number b, which is z percent less than a itself. If a is increased by z percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a | [
"I only",
"II only",
"III only",
"I and II only",
"II and III only"
] | Let q = 10% then z = 100/11 %
let b = 100 then a = 110
after increasing a by z and decreasing by q we get c= 108
therefore c<a
C it is answer
The answer is: C | C |
mathematics | If m is the average (arithmetic mean) of the first 10 positive multiples of 6 and if M is the median of the first 10 positive multiples of 6, what is the value of M β m ? | [
"β5",
"10",
"5",
"0",
"27.5"
] | The first 10 positive multiples of 6 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is:in any evenly spaced set the arithmetic mean (average) is equal to the median.
Hence M=m --> M-m=0.
Answer: D.
The answer is: D | D |
mathematics | The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum. | [
"Rs.17277",
"Rs.17000",
"Rs.17287",
"Rs.172827",
"Rs.172711"
] | Explanation:
The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
Answer: B
The answer is: B | B |
mathematics | In a certain company, the ratio of the number of managers to the number of non-managers in any department must always be greater than 7 : 32. In the company, what is the maximum number of non-managers in a department that has 9 managers? | [
"39",
"40",
"41",
"42",
"43"
] | 9/7 * 32 = 41.1
The answer is C.
The answer is: C | C |
mathematics | In a two-digit, if it is known that its unitβs digit exceeds its tenβs digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is: | [
"24",
"26",
"42",
"46",
"None"
] | EXPLANATION
Let the tenβs digit be x.
Then, unitβs digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x β 140 = 0
11x2 + 13x β 70 = 0
(x β 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
Answer A
The answer is: A | A |
mathematics | You are renting an apartment and you need β900 for each side, how many feet are you looking to measure? | [
"21",
"22",
"23",
"25",
"30"
] | Try filling the numbers into the answer y x y =
Find the closest to 900.
Answer E
The answer is: E | E |
mathematics | Calculate the value of 2.71 x 10^9 ? | [
"2710000000",
"271000",
"2710000",
"27100000",
"271000000"
] | 2.71 x 10^9 = 2.71 x 1000000000 = 2710000000.
Answer = A
The answer is: A | A |
mathematics | How much interest can a person get on Rs. 8600 at 17.5% p.a. simple interest for a period of two years and six months? | [
"3587.58",
"3587.59",
"3587.5",
"3762.5",
"3587.56"
] | I = (8600 * 2.5 * 17.5)/100 = (8600 * 5 * 35)/(100 * 2 * 2) = Rs. 3762.50.Answer: D
The answer is: D | D |
mathematics | Brand X coffee costs twice as much as brand Y coffee. If a certain blend is 1/4 brand X and 3/4 brand Y. what fraction of the cost of the blend is Brand X? | [
"a. 2/5",
"b. 1/5",
"3. 1/2",
"4. 2/3",
"5. 3/4"
] | Assume Cost of X= Cx = 200 , Cost of Y = Cy=100
The blend contains 0.25 X and 0.75 Y ---> Cost of the blend = Cbl = 0.25*200+0.75*100= 125
Thus fraction of X in the blend = 0.25*200/125 = 2/5.
Answer : A
The answer is: A | A |
mathematics | The average of six numbers is X and the average of three of these is Y.If the average of the remaining three is z, then | [
"x = y + z",
"2x = y + z",
"x = 2y + z",
"x = y + 2z",
"None of these"
] | Explanation:
X =((3y+3z)/6)
or
2X= y + z
Option B
The answer is: B | B |
mathematics | The cross-section of a tunnel is a trapezium in shape. If the tunnel is 15 m wide at the top and 5 m wide at the bottom and the area of cross-section is 400 sq m, the depth of tunnel is? | [
"200 m",
"600 m",
"400 m",
"800 m",
"900 m"
] | 1/2 * d (15 + 5) = 400
d = 400
ANSWER:C
The answer is: C | C |
mathematics | 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work? | [
"16",
"18",
"24",
"22",
"26"
] | C
24
Let the required number of days be x.
Less men, More days (Indirect Proportion)
27 : 36 :: 18 : x <-> 27 x x = 36 x 18
x = (36 x 18)/27
x = 24
The answer is: C | C |
mathematics | In a college the ratio of the numbers of boys to the girls is 8:5. If there are 120 girls, the total number of students in the college is? | [
"312",
"356",
"452",
"416",
"512"
] | Let the number of boys and girls be 8x and 5x
Then , 5x = 120
x= 24
Total number of students = 13x = 13*24 = 312
Answer is A
The answer is: A | A |
mathematics | A cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm. Find the total area of the wet surface. | [
"66 m square",
"49 m square",
"77 m square",
"44 m square",
"33 m square"
] | Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(4*1.25+6*1.25)]+6*4 = 49 m square
Answer: B
The answer is: B | B |
mathematics | A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? | [
"675, Rs.1350",
"575, Rs.1350",
"1350, Rs.675",
"1450, Rs.675",
"None"
] | Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
ANSWER:A
The answer is: A | A |
mathematics | B and C started a business investing Rs. 72,000 and Rs. 45,000 respectively. In what ratio the profit earned after 7 years be divided between B and C respectively? | [
"7:5",
"5:8",
"5:7",
"8:5",
"None of these"
] | B:C = 72000 : 45000 = 8:5.
ANSWER:D
The answer is: D | D |
mathematics | In 1970 there were 8,902 women stockbrokers in the United States. By 1978 the number had increased to 19,947. Approximately what was the percent increase? | [
"45%",
"125%",
"145%",
"150%",
"225%"
] | We can use approximation to get the answer quickly.
Like,
19,947 is approx 20000
8902 is approx 8900
So, Total increase = 20000 - 8900 = 11100
Hence, % increase = 11100 / 8900 = approx. 11/9 = 1.22 = approx. 1.25
So, Choice is B.
The answer is: B | B |
mathematics | The distance between Delhi and Mathura is 140 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet? | [
"10.50 a.m.",
"10.40 a.m.",
"10.30 a.m.",
"11.40 a.m.",
"1.40 a.m."
] | D = 140 β 20 = 120
RS = 20 + 25 = 45
T = 120/45 = 2 2/3 hours
8 a.m. + 2 hrs 40 min = 10.40 a.m.
ANSWER:B
The answer is: B | B |
mathematics | The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit? | [
"1000",
"3000",
"2000",
"4000",
"5000"
] | B
2000
Let C.P. be $x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000.
The answer is: C | C |
mathematics | The average age of a group of 12 students is 20years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is | [
"22",
"23",
"24",
"25",
"26"
] | total age of 12 std=20*12
total age of 16 std=21*16
total age of 4 std=(21*16)-20*12=96
avg of 4 std =(96)/4=24
ANSWER:C
The answer is: C | C |
mathematics | A bag contains 6 red, 4 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? | [
"1/13",
"2/23",
"5/26",
"5/22",
"3/23"
] | P(Both are red),
=6C212C2=6C212C2
=15/66=5/22
D
The answer is: D | D |
mathematics | The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 588, Krishan has ? | [
"s. 2890",
"s. 2330",
"s. 1190",
"s. 3468",
"s. 2680"
] | Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 588 : N
&there N = 289 x 588 / 49
= Rs. 3468
Answer :D
The answer is: D | D |