question stringlengths 10 716 | options listlengths 4 4 | answer stringclasses 4 values | correct_option stringlengths 1 63 | explanation stringlengths 0 2.6k | dataset stringclasses 3 values |
|---|---|---|---|---|---|
The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is? | [
"887",
"267",
"342",
"276"
] | C | 342 | 400*(90/100)*(95/100)
= 342
Answer: C | aqua_rat |
What is the remainder when you divide 2^200+2 by 7? | [
"1",
"2",
"3",
"6"
] | D | 6 | answer is D. this is very similar to the 32^32^32+2 divided by 7 question. | aqua_rat |
The G.C.D of 1.08, 0.42 and 0.9 is | [
"0.19",
"0.1",
"0.06",
"0.11"
] | C | 0.06 | Explanation:
Given numbers are 1.08 , 0.42 and 0.90
H.C.F of 108, 42 and 90 is 6 [because G.C.D is nothing but H.C.F]
therefore H.C.F of given numbers = 0.06
Answer: C) | aqua_rat |
If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle. | [
"110",
"120",
"130",
"140"
] | B | 120 | Explanation:
let length = x and breadth = y then
2(x+y) = 46 => x+y = 23
x²+y² = 17² = 289
now (x+y)² = 23²
=>x²+y²+2xy= 529
289+ 2xy = 529
=> xy = 120
area =xy=120 sq. cm Answer: B | aqua_rat |
Average of 15 results is 43. If the average of first seven results is 41 and average of last seven results is 45 Then find the eighth result? | [
"41",
"39",
"43",
"45"
] | C | 43 | Option 'C' | aqua_rat |
In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N) | [
"L(L-N) /L-M",
"L(N-M) / L-M",
"L-N",
"M-N"
] | A | L(L-N) /L-M | the ans is quite simple N-M but since the ans is not given, the best way to 'find' the correct option is to plug in the numbers. For my work, i took the following numbers:
L = 200
M = 10
N =20.
So basically, L beat G by 20 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, A.
Out of which, i choose A. | aqua_rat |
A train starts from Delhi at 6.00 a.m. and reaches Meerut at 10 a.m. The other train starts from Meerut at 8 a.m. and reaches Delhi at 11.30 a.m. If the distance between Delhi and Meerut is 200 km, then at what time did the two trains meet each other? | [
"8.56 a.m",
"8.46 a.m",
"7.56 a.m",
"8.30 a.m"
] | A | 8.56 a.m | The Speed of the train starting from Delhi = 200/4 = 50 km/h
The Speed of train starting from Meerut = 200/3.5 = 400/7 km/h
Suppose the two trains meet x hours after 6.00 am
Then x X 50 + (x - 2) x 400/7 = 200
or, 350x + 400x - 800 = 1400
or, 750x = 2200
or, x = 2200/750 = 2h 56 min
Hence, the required time = 8.56 am
ANSWER:A | aqua_rat |
Robin's average (arithmetic mean) test score on 9 tests is 82. What must be Robin's score on a 10th test for his average score on the 10 tests to be 83? | [
"92",
"82",
"72",
"62"
] | A | 92 | (9*82+x)/10=83
x=(10*83)-(9*82)
x= 830 - 738
total score required 830 - 738=92
Correct answer is A | aqua_rat |
If T = 5/9 * (K - 32), and if T = 20, then what is the value of K? | [
"68",
"70",
"72",
"74"
] | A | 68 | K-32=9T/5
K=9T/5 + 32
K=9(20)/5 + 32 = 68
The answer is A. | aqua_rat |
The average of 5 numbers is 7.4. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 9.2. What number is multiplied by 3? | [
"1.5",
"3.0",
"3.9",
"4.5"
] | D | 4.5 | The average of 5 numbers is 7.4
The sum of 5 numbers will be 7.4 x 5 = 37
The average of 5 number after one of the number is multiplied by 3 is 9.2
The sum of the numbers will now be 9.2 x 5 = 46
So the sum has increased by 46-37 = 9
Let the number multiplied by 3 be n
Then,
3n = n+9
or 2n = 9
or n = 4.5
Answer:- D | aqua_rat |
A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is? | [
"11",
"67",
"88",
"25"
] | D | 25 | [50/x + 50/(x/2)] – 100/x = 2
x = 25
Answer:D | aqua_rat |
A lady bought five books namely A,B,C,D,E to distribute her 3 child. How many ways she can distribute books? | [
"3^3",
"3^4",
"3^5",
"3^6"
] | C | 3^5 | 3*3*3*3*3
3^5
ANSWER:C | aqua_rat |
The difference between compound interest and simple interest on an amount of $15,000 for 2 years is $96. What is the rate of interest per annum? | [
"6%",
"7%",
"9%",
"8%"
] | D | 8% | [15000 x (1 + R/100)^2 - 15000] - [(15000 x R x 2)/100] = 96
==> 15000[(1 + R/100)^2 - 1 - 2R/100] = 96
==> 15000[((100 + R)^2 - 10000 - (200 x R))/10000] = 96
==> R^2 = (96 x 2)/3 = 64
==> R = 8. Rate = 8%
Answer D)8% | aqua_rat |
In expressing a length 81.469 km as nearly as possible with three significant digits, find the percentage error? | [
"0.075%",
"0.156%",
"0.034%",
"0.038%"
] | D | 0.038% | Error = 81.5-81.469 = 0.031
Required percentage = (0.031/81.469)*100 = 0.038%
Answer is D | aqua_rat |
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is: | [
"10 d",
"0 d",
"15 d",
"5 d"
] | A | 10 d | Angle traced hr 13/3 = (360/12 * 13/3) = 130
traced by min hand 20 min = (360/60*20) = 120
req = (130-120) = 10 d
ANSWER A | aqua_rat |
If p and y are both odd prime numbers and p < y, how many distinct positive integer factors does 2py have? | [
"3",
"4",
"6",
"8"
] | D | 8 | Since 2py prime factors are p^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer. | aqua_rat |
What are resources that don't run out? | [
"residual resources",
"general resources",
"orbital resources",
"renewable resources"
] | D | renewable resources | Renewable resources can be renewed as they are used. An example is timber , which comes from trees. New trees can be planted to replace those that are cut down. Sunlight is a renewable resource. It seems we will never run out of that! What are some other renewable resources?. | science |
Hydrostatic skeletons are well suited for life in what kind of environments? | [
"pelagic",
"aquatic",
"bacterial",
"surface"
] | B | aquatic | science | |
A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A. | [
"100",
"110",
"120",
"140"
] | C | 120 | In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.
x/6 = (30+x)/8
x = 90. So distance from start after which B will catch A = 90+30 =120km Answer : C | aqua_rat |
Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is? | [
"5",
"6",
"1",
"7"
] | A | 5 | 2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer: A | aqua_rat |
If a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet, what is the length of each of the shorter sides? | [
"4",
"7",
"8",
"13"
] | C | 8 | This question can be solved algebraically or by TESTing THE ANSWERS.
We're told that a rectangle has an area of 120 and a perimeter of 46. We're asked for the length of one of the SHORTER sides of the rectangle.
Since the answers are all INTEGERS, and the area is 120, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 120,
Let's TEST Answer C: 8
IF...
The shorter side = 8...
The area = 120....120/8 = 15 = the longer side
Perimeter = 8+8+15+15 = 46
C | aqua_rat |
Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 400 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby? | [
"1:40 PM",
"1:50 PM",
"2:00 PM",
"2:10 PM"
] | C | 2:00 PM | Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.
Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 80t: 400+60t=80t-200 --> t=30.
1:30 PM + 30 minutes = 2:00 PM.
Answer: C. | aqua_rat |
How much interest can a person get on Rs. 7200 at 17.5% p.a. simple interest for a period of two years and six months? | [
"Rs. 4150",
"Rs. 3850",
"Rs. 3770",
"Rs. 3150"
] | D | Rs. 3150 | I = (7200 * 2.5 * 17.5)/100 = (7200 * 5 * 35)/(100 * 2 * 2)
= Rs. 3150
ANSWER:D | aqua_rat |
In the decimal expansion of (2/5)^8 what is the eighth digit to the right of the decimal point? | [
"6",
"5",
"4",
"3"
] | A | 6 | Step 1 Convert fraction to decimal with two decimal places 2/5 = 0.40 then convert to scientific number = 4*10^-1
Step 2 Multiply 4^8 by 10^-8
Step 3 4 has the sequence 4, 16, 64
Answer is A | aqua_rat |
Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4,3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (4,3). What would be the exact root of the original quadratic equation ? | [
"(6, 1)",
"(-3,-4)",
"( 4, 3)",
"(-4, -3)"
] | A | (6, 1) | Explanation :
Equation of quadratic equation is
ax2 + bx + c = 0 .
x2 + bx + c = 0 . First roots = (4, 3)
Sum of the roots -b / a = -7 .
=> b = 7.
Product of the roots = c / a = 12.
=> c =12.
∴ Equation formed x2 – 7b + 12 = 0 ............ (i)
Another boy gets the wrong roots (2, 3).
∴ Sum of the roots = -b / a = -5.
=> b = 5.
Products of the roots = c / a = 6.
=> c = 6.
Equation formed x2 – 5b + 6 = 0 ............ (ii)
x2 + b′x + c1 = 0.
b′ = 2 + 3 .
∴ c = 6
Hence, x2 – 7x + 6 = 0.
=> x2 – 6x – x + 6 = 0.
=> x(x – 6) – 1(x – 6) = 0.
=> (x – 6)(x – 1) = 0.
∴ x = 6, 1.
Hence, the actual roots = (6, 1).
Answer : A | aqua_rat |
The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 285, then the mean profit for the last 15 days would be | [
"Rs. 200",
"Rs. 350",
"Rs. 275",
"Rs. 415"
] | D | Rs. 415 | Average would be : 350 = (285 + x)/2
On solving, x = 415.
Answer: D | aqua_rat |
The smallest 3 digit prime number is | [
"A)113",
"B)103",
"C)109",
"D)101"
] | D | D)101 | The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
D) | aqua_rat |
P and Q started a business investing Rs 10000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively. | [
"2:7",
"2:6",
"17:6",
"2:3"
] | D | 2:3 | Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 10000:15000
= 10:15
= 2:3
Option D | aqua_rat |
A can do a half of certain work in 70 days and B one third of the same in 35 days. They together will do the whole work in. | [
"17 days",
"97 days",
"19 days",
"60 days"
] | D | 60 days | A = 140 days
B = 105 days
1/140 + 1/105 = 7/420 = 1/60
=>60 days
Answer: D | aqua_rat |
Find the odd man out
5,15,45,60,90,180 | [
"60",
"180",
"90",
"5"
] | A | 60 | 5*3= 15
15*3 =45
45*2=90
90*2=180
180*2=360
ANSWER:A | aqua_rat |
A tap can fill a tank in 12 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely? | [
"1 hr 20 min",
"4 hr",
"6 hr",
"8 hr 00 min"
] | D | 8 hr 00 min | Explanation:
1 tap can fill the tank in 12 hours.
Therefore
1 tap can fill half tank in 6 hours.
3 taps can fill the tank in 12/3 hour = 4 hours.
Therefore
3 taps can fill half tank in 4/2 hour = 2 hours.
Total time taken=8 hour 00 minutes
Answer: Option D | aqua_rat |
If 2/3 of the air in a tank is removed with each stroke of a vacuum pump, how many strokes does it take before less than 1% of the original amount of air in the tank remains? | [
"2",
"3",
"4",
"5"
] | D | 5 | My approach is to find more or less good number and plug in. Lets take 90 as the total volume of an air, and the question asks after how many stokes there will be less than 0,9 air in a tank, if each stroke takes 2/3 of an air.
So after he1 strokethe volume will be 30 (90-60=30), and so on
2 stroke- 30-20=10
3 stroke- 10-6,7=3,3
4 stroke- 3,3-2,2=1,1
5 stroke- 1,1 - minus something that gets us less than 0,9 for sure. so the answer is: after 5 strokes there will be less than 1% of air left in a tank. OptionD. | aqua_rat |
A committee has 6 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee? | [
"127",
"300",
"882",
"272"
] | B | 300 | The number of ways to select two men and three women
= 6C₂ * ⁶C₃
= (6*5)/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 300
Answer: B | aqua_rat |
The difference between the number and its three fifth is 40, what is the number? | [
"80",
"100",
"90",
"120"
] | B | 100 | Explanation:
Let the number be x. Then,
x - (3/5)x = 40
(2/5)x = 40
x = (40 x 5)/2 = 100
Answer: Option B | aqua_rat |
Simplify: 256 x 256 - 144 x 144 | [
"761200",
"44800",
"761800",
"761500"
] | B | 44800 | (256)^2 - (144)^2 = (256 + 144) (256 - 144) = 400 x 112 = 44800
Answer is B | aqua_rat |
In how many ways Chief Minister and Minister be elected from a team of 14 members? | [
"182",
"131",
"132",
"143"
] | A | 182 | To do this, if captain is elected first, then we have 14 ways of doing this.
For election of vice-captain, we have only 13 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 14*13 = 182 ways.
Answer : A | aqua_rat |
Atoms of one element can be transformed into another through which process? | [
"magnetic reactions",
"longer reactions",
"developed reactions",
"nuclear reactions"
] | D | nuclear reactions | Not all atoms of an element must have precisely the same mass. Atoms of one element can be transformed into another through nuclear reactions. The compositions of many solid compounds are somewhat variable. Under certain circumstances, some atoms can be divided (split into smaller particles). These modifications illustrate the effectiveness of the scientific method; later experiments and observations were used to refine Dalton’s original theory. | science |
The banker’s discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is | [
"210",
"280",
"360",
"450"
] | C | 360 | Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[72 * 60 / 72 - 60] = Rs. [72 * 60 / 12] = Rs. 360.
Answer C | aqua_rat |
If y is a positive number and 1/2 the square root of x is the cube root of y, then y= | [
"64",
"32",
"16",
"4"
] | A | 64 | 1/2 the square root of x is cube root of y.
if y= 64..
then 1/2 the square root of y= 4 and cube of y is 64.
Option A. | aqua_rat |
A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is : | [
"253",
"366",
"298",
"266"
] | A | 253 | Explanation:
Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352
Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit.
Hence, required number = 253.
Answer: A) 253 | aqua_rat |
Cal wants to invest Rs. 50000 at the local bank that offers a rate of 12% per annum per year. If the interest is compounded monthly, how much will Cal get at the end of 3 years? | [
"71534.84",
"71534.48",
"71538.44",
"71543.84"
] | C | 71538.44 | P = Rs. 50000; R = 12% p.a. = 1% per month; T = 3 years = 36 months
Amount = [50000 * (1 + 1/100)36]
= (50000 * (1.01)36) = Rs. 71538.44
Answer: C | aqua_rat |
The difference between a number and its three fifth is 50. What is the number? | [
"75",
"100",
"125",
"175"
] | C | 125 | Sol.
Let the numbers be x.
Then, x-3/5x = 50
⇔2/5x = 50⇔ x = (50x5/2) = 125.
Answer C | aqua_rat |
If A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time | [
"0.49",
"0.48",
"0.41",
"0.482"
] | B | 0.48 | Explanation:
Probability that A speaks truth is 80/100 = 0.8
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.8 × 0.6 = 0.48
Answer: B | aqua_rat |
In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ? | [
"21",
"22",
"23",
"24"
] | D | 24 | n(A)=(60/100 ∗96)=288/5
n(B)=(30/100 ∗96)=144/
n(A∩B)=(15/100 ∗96)=72/5
People who have either or both lunchn(A∪B)=288/5 +144/5 −72/5 =360/5 =72
So People who do no have either lunch were = 96 -72 = 24 ANSWER : D | aqua_rat |
138.009 + 341.981 – 146.305 = 123.6 + ? | [
"120.085",
"120.85",
"220.085",
"None of these"
] | D | None of these | Solution
Let 138.009 + 341.981 - 146.305 = 123.6 + x.
Then, x = (138.009 + 341.981) - (146.305 + 123.6) = 479.99 - 269.905 = 210.085 . Answer D | aqua_rat |
Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 125 mangoes. | [
"360",
"380",
"400",
"416"
] | D | 416 | Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 125 mangoes = 125*3.33 = 416.
Answer D | aqua_rat |
The standard reduction potential can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at this? | [
"electrode",
"cathode",
"Spinner",
"plasma"
] | B | cathode | The standard reduction potential can be determined by subtracting the standard reduction potential for the reaction occurring at the anode from the standard reduction potential for the reaction occurring at the cathode. The minus sign is necessary because oxidation is the reverse of reduction. E°cell = E°cathode − E°anode +0.34 V = E° 2+ − E°H + /H = E° 2+ − 0 = E° Cu. | science |
The cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paise per meter is Rs. 36. The breadth of the room is ? | [
"6 meters",
"7 meters",
"8 meters",
"9 meters"
] | A | 6 meters | Length of carpet = Total Cost / Rate
= 3600 / 30
= 120 m
Area of carpet = (120 x 75) / 100 m2
= 90 m2
∴ Area of the room = 90 m2
Breadth of the room = Area /Length
= 90 / 15 m
= 6m
Answer : A | aqua_rat |
In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that at least 1 women is included in the committee | [
"40",
"46",
"52",
"54"
] | B | 46 | 1W 2M 2W 1M 3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
At least one women = total - with out women
At least one women = 56 - 10 = 46
B) | aqua_rat |
Excluding stoppages, the speed of a bus is 84 kmph and including stoppages, it is 70 kmph. For how many minutes does the bus stop per hour? | [
"12 min",
"10 min",
"15 min",
"14 min"
] | B | 10 min | Due to stoppages, it covers 14 km less.
Time taken to cover 14 km = (14/84 x 60) min = 10 min
Answer : B | aqua_rat |
Look at this series: V, VIII, __, XIV, XVII, XX, ... What number should fill the blank? | [
"IX",
"XXIII",
"XV",
"XI"
] | D | XI | Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D | aqua_rat |
The average length of a woman’s menstrual cycle is what? | [
"5 days",
"16 days",
"19 days",
"28 days"
] | D | 28 days | The Menstrual Cycle Now that we have discussed the maturation of the cohort of tertiary follicles in the ovary, the build-up and then shedding of the endometrial lining in the uterus, and the function of the uterine tubes and vagina, we can put everything together to talk about the three phases of the menstrual cycle—the series of changes in which the uterine lining is shed, rebuilds, and prepares for implantation. The timing of the menstrual cycle starts with the first day of menses, referred to as day one of a woman’s period. Cycle length is determined by counting the days between the onset of bleeding in two subsequent cycles. Because the average length of a woman’s menstrual cycle is 28 days, this is the time period used to identify the timing of events in the cycle. However, the length of the menstrual cycle varies among women, and even in the same woman from one cycle to the next, typically from 21 to 32 days. Just as the hormones produced by the granulosa and theca cells of the ovary “drive” the follicular and luteal phases of the ovarian cycle, they also control the three distinct phases of the menstrual cycle. These are the menses phase, the proliferative phase, and the secretory phase. | science |
If the sum of two numbers is 22 and the sum of their squares is 404, then the product of the numbers is | [
"40",
"44",
"80",
"88"
] | A | 40 | according to the given conditions x+y = 22
and x^2+y^2 = 404
now (x+y)^2 = x^2+y^2+2xy
so 22^2 = 404 + 2xy
so xy = 80/2 = 40
ANSWER:A | aqua_rat |
The triplicate ratio of 1:2 is? | [
"1:7",
"1:8",
"1:3",
"1:1"
] | B | 1:8 | 13: 23 = 1:8
Answer: B | aqua_rat |
There are 9 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played? | [
"10",
"30",
"36",
"60"
] | C | 36 | 9 players are there.
two players play one game with one another.
so 9C2=9x8/2=36
SO OPTION C is correct | aqua_rat |
If m is the average (arithmetic mean) of the first 10 positive multiples of 3 and if M is the median of the first 10 positive multiples of 3, what is the value of M – m ? | [
"–5",
"5",
"0",
"25"
] | C | 0 | The first 10 positive multiples of 3 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: C. | aqua_rat |
How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/53 ? | [
"6",
"3",
"2",
"1"
] | C | 2 | There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.
So, we start with
a=1, we get b as -ve. out
a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)
a=3, we get b as 3. Yes (Now we have 3 possible solutions)
a=4, we get b as fraction. Out
a=5, we get b again as some fraction. Out
a=6 already taken.
We have A,B options left. C,D,E are out.
A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.
When a=b, we have only 1 solution = 3. So, one more solution, where a=b is not possible.
So, answer will be C. | aqua_rat |
My brother is 2 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 1 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born? | [
"32 yrs, 23 yrs",
"30 yrs, 25 yrs",
"35 yrs, 29 yrs",
"35 yrs, 33 yrs"
] | B | 30 yrs, 25 yrs | Sol.
Clearly, my brother was born 2 years before I was born and 1 years after my sister was born.
So, father's age when brother was born = (28 + 2) = 30 years.
mother's age when was born = (26 - 1) years = 25 years.
Answer B | aqua_rat |
In what ratio water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per litre? | [
"2:7",
"1:2",
"2:9",
"2:2"
] | B | 1:2 | Answer with Explanation: By the rule of allegation, i. C.P of 1 liter of water = 0 ii. C.P of 1 liter of milk = 12 iii. Mean price (p) = 8 iv. d – m = 12-8 = 4 v. m – c = 8-0 = 8 Ratio of water and milk = 4 : 8 = 1 : 2
Answer:B | aqua_rat |
If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 50 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day? | [
"100",
"120",
"140",
"150"
] | A | 100 | Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+50)=(R+5)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=100
Ans A | aqua_rat |
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle? | [
"16",
"15",
"12",
"87"
] | C | 12 | Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s
= 12∏ cm.
Answer:C | aqua_rat |
Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 15 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today? | [
"40",
"48",
"43",
"45"
] | D | 45 | Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 45 (the only option that is a multiple of 3).
Then age of Lyn would be 15. In 15 yrs, Ele would be 60 and Lyn would be 30 - so Lyn would be half as old as Ele.
Answer (D) | aqua_rat |
If the average of 20,21, 23, 24, 25, 28, 28, 29, 31 and x is 26, what is the value of x? | [
"26",
"28",
"30",
"31"
] | D | 31 | Sum of the deviations of the numbers in the set from the mean is always zero
20, 21, 23, 24, 25, 28, 28, 29, 31
mean is 26
so the list is -6-5-3-2-1+2+2+3+5... this shud total to zero
but this is -5 , hence we need a number that is 5 more than the mean to get a +5 and make it zero
hence the answer is 26 + 5 = 31
D | aqua_rat |
What french chemist discovered the radioactive elements polonium and radium? | [
"marie curie",
"pascal curie",
"margaret curie",
"louis pasteur"
] | A | marie curie | Another scientist, who worked with Becquerel, actually came up with the term radioactivity . The other scientist was the French chemist Marie Curie. She went on to discover the radioactive elements polonium and radium. She won two Nobel Prizes for her discoveries. You can learn more about Marie Curie at this URL: http://nobelprize. org/nobel_prizes/physics/laureates/1903/marie-curie-bio. html. | science |
How many of the positive divisors of 600 are also multiples of 4 not including 600? | [
"6",
"8",
"9",
"11"
] | D | 11 | 600 = 2^6 * 3 * 5 = (4) * 2 * 3 * 5^2
Besides (4), the exponents of 2, 3, and 5 are 1, 1, and 2.
There are (1+1)(1+1)(2+1) = 12 ways to make multiples of 4.
We must subtract 1 because one of these multiples is 600.
The answer is D. | aqua_rat |
A man goes downstream at 12 kmph, and upstream8 kmph. The speed of the stream is | [
"2kmph",
"4kmph",
"16kmph",
"2.5kmph"
] | A | 2kmph | Speed of the stream = 1/2(12-8)kmph
=2kmph.
correct option A | aqua_rat |
A bag contains 10 red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability E that all 3 jellybeans removed from the bag are blue? | [
"9/100",
"2/19",
"1/8",
"3/20"
] | B | 2/19 | Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability E= 120 / 1140 = 2/19
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option B | aqua_rat |
If p=125×243×16/405, how many digits are in p? | [
"1",
"2",
"3",
"4"
] | D | 4 | p = 125 * 243 * 16 / 405
p= 5^3 * 3 * 9^2 * 4^2 / (5 * 9^2)
p= 5^2 * 3 * 4^2
p = 20^2 * 3 = 1200
answer D | aqua_rat |
running turns carbohydrates into | [
"fat",
"sweat",
"motion and heat",
"protein"
] | C | motion and heat | science | |
How many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph? | [
"26",
"72",
"25",
"82"
] | A | 26 | Explanation:
D = 100 + 160 = 260
S = 36 * 5/18 = 10 mps
T = 260/10 = 26 sec
Answer: Option A | aqua_rat |
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs.24. The present worth is | [
"Rs. 480",
"Rs. 520",
"Rs. 600",
"Rs. 960"
] | C | Rs. 600 | Solution
T.D = (B.G x 100/Rate x Time)
= Rs.(24x100 / 10x 2)
= Rs.120.
P.W = (100 x T.D/Rate x Time)
= Rs.(100x120 / 10x 2)
= Rs.600.
Answer C | aqua_rat |
Conducting wires have a small degree of what? | [
"insulation",
"heat",
"electrical resistance",
"magnetism"
] | C | electrical resistance | Conducting wires have a small electrical resistance. The electrical resistance of a conducting wire is related to the type of metal used and inversely related to the cross-sectional area of the wire. The larger the diameter of a wire, the greater the cross-sectional area, and the lower the electrical resistance will be. When electrons flow through a wire, they repel each other and interfere with the passage of other electrons. If there are a very large number of electrons passing through a wire with small diameter, the electrons will experience a greater resistance than if the wire diameter were larger and the electrons had more space between them. | science |
A man is 40 years older than his son. In six years, his age will be twice the age of his son. The present age of this son is | [
"31 years",
"32 years",
"33 years",
"34 years"
] | D | 34 years | Explanation:
Let's Son age is x, then Father age is x+40.
=> 2(x+6) = (x+40+6)
=> 2x+12 = x+46
=> x = 34 years
Answer: Option D | aqua_rat |
A certain candy store sold lollipops for $0.90 each and pieces of individually wrapped saltwater taffy for $0.20 each. If a customer purchased both lollipops and taffy from the store, and spent a total of $3.90, what total number of lollipops and saltwater taffy did the customer purchase? | [
"6",
"7",
"8",
"9"
] | D | 9 | we can take numbers, as price of lollipop 9, 2 for taffy and 39 total for ease.
Now we can determine quickly that total number should range between 39/9 <= N <=39/2, so ans should be between 4 and 20.
Now solving the expression 9A+2B =39
first possibility with 1 lollipop, 15 taffy we get $3.90 total amount, but 1+15=16, and 16 is not an option.
So next choice, for 9A+2B =39 would come by decreasing 39 in multiple of 9 and checking divisibility of that number by 2. this way we get
3 lollipop, 6 taffy would be $3.90 total, 3*0.90 + 6*0.20= 3.90
Hence total number is 3 + 6 = 9
Ans D | aqua_rat |
A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet? | [
"229",
"288",
"600",
"888"
] | C | 600 | D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km
Answer: C | aqua_rat |
Each shelf of a bookcase contains 20 books. If the librarian took out 42 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have? | [
"A)4",
"B)12",
"C)6",
"D)8"
] | B | B)12 | Denoting x the number of the shelves,
we can build an equation: 20x=16(x−1)+22+42
Solving the equation, we get x=12
Answer: B | aqua_rat |
Carol spends 1/4 of her savings on a stereo and 1/3 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television? | [
"1/4",
"2/7",
"5/12",
"1/2"
] | C | 5/12 | Total Savings = S
Amount spent on stereo = (1/4)S
Amount spent on television = (1-1/3)(1/4)S = (2/3)*(1/4)*S = (1/6)S
(Stereo + TV)/Total Savings = S(1/4 + 1/6)/S = 5/12
Answer: C | aqua_rat |
Diesel costs Rs.4per lit and petrol costs 5.63 per litre. If the price of diesel rise by 10% a month and the price of petrol is unchanged.How many months will it take until a litre of Diesel costs more than a litre of petrol. | [
"9 months",
"5 months",
"6 months",
"4 months"
] | D | 4 months | Explanation :
=>In the First Month the price of the diesel would be 4*110/100 = 4.4
=>In the Second Month the price of the diesel would be 4.4*110/100 = 4.84
=>In the Third Month the price of the diesel would be 4.84*110/100 = 5.324
=>In the fourth Month the price of the diesel would be 5.324*110/100 = 5.85 which is higher than the
price of the petrol!
Answer : D | aqua_rat |
The sloth's lack of urgency is a great example of | [
"stimuli",
"adaptation",
"movies",
"adoption"
] | B | adaptation | science | |
Jamal had a bag of marbles. He had 12 yellow, 10 blue, 5 green and 1 black marbles. He decided to randomly select a ball from the bag. What is the proabilitly that he will draw a black marble? | [
"10/28",
"1/28",
"12/28",
"28/1"
] | B | 1/28 | B | aqua_rat |
What is the study of energy and how it interacts with matter? | [
"kinetics",
"cosmology",
"physics",
"quantum mechanics"
] | C | physics | Physics is the study of energy and how it interacts with matter. Important concepts in physics include motion, forces such as magnetism and gravity, and different forms of energy. Physics concepts can answer all the questions on the right page of the notebook in Figure above . | science |
The top and bottom of a tower were seen
to be at angles of depression 30° and 60° from the top of a
hill of height 100 m. Find the height of the tower | [
"64.67 m",
"66.67 m",
"68.67 m",
"56.67 m"
] | B | 66.67 m | By making A diagram
AC represents the hill and DE represents the pole
Given that AC = 100 m
angleXAD = angleADB = 30° (∵ AX || BD )
angleXAE = angleAEC = 60° (∵ AX || CE)
Let DE = h
Then, BC = DE = h, AB = (100-h) (∵ AC=100 and BC = h), BD = CE
tan 60°=ACCE=>3√=100CE=>CE = 1003√--- (1)
tan 30°=ABBD=>13√=100−hBD=>13√=100−h(1003√)
(∵ BD = CE and Substituted the value of CE from equation 1 )=>(100−h)=13√×1003√=1003=33.33=>h=100−33.33=66.67 m
i.e., the height of the pole = 66.67 m
ANSWER:B | aqua_rat |
If something is alive, then it requires | [
"something to keep it interested",
"a source to propel it forward",
"something to give it hope",
"something to consider doing"
] | B | a source to propel it forward | science | |
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5? | [
"1/2",
"2/5",
"8/5",
"9/20"
] | D | 9/20 | Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.
ANSWER : D | aqua_rat |
what causes water to evaporate more quickly by adding heat? | [
"distant stars",
"our star",
"sunlight",
"Solar energy"
] | B | our star | our star causes water to evaporate more quickly by adding heat | qasc |
Insulin is a hormone that helps absorb what from the blood? | [
"hormones",
"blood cells",
"glucose",
"Energy"
] | C | glucose | Insulin is a hormone that helps cells absorb glucose from the blood. | qasc |
The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers? | [
"5",
"7",
"8",
"9"
] | A | 5 | Explanation:
A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
A) | aqua_rat |
If x is 12 percent greater than 80, then x = | [
"89.6",
"91.0",
"88.0",
"70.9"
] | A | 89.6 | 12% of 80 = (80*0.12) = 9.6
12% greater than 80 = 80 + 9.6 = 89.6
Answer is clearly A. | aqua_rat |
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 9 candidates for the 4 consultant slots. If 2 out of 9 consultants refuse to be on the same team, how many different teams are possible? | [
"540",
"630",
"740",
"820"
] | B | 630 | Answer= Total number combinations - Total number of combinations with constraints
Total number of combinations = 2C1*3C1*9C4= 756
Total number of combinations with constraints = 2C1*3C1*7C2=126
Answer=756-126=630
ANSWER: B | aqua_rat |
The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 10 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each? | [
"s.9060",
"s.4520",
"s.4527",
"s.4530"
] | A | s.9060 | Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 10
= Rs.9060
Answer:A | aqua_rat |
The probability that a number selected at random from the first 50 natural numbers is a composite number is ? | [
"17/28",
"17/25",
"17/17",
"17/19"
] | B | 17/25 | The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50
= 17/25.
Answer:B | aqua_rat |
In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m ? | [
"127.5 m",
"254 m",
"184 m",
"212 m"
] | A | 127.5 m | Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 x 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C
= (600 x 212.5)/1000 = 127.5 m.
ANSWER IS A | aqua_rat |
Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 30 days. | [
"16 days.",
"17 days.",
"18 days.",
"19 days."
] | C | 18 days. | They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 30*6/10 = 18 days.
ANSWER:C | aqua_rat |
Spores are generally produced through what type of reproduction? | [
"sexual",
"similar",
"hormone",
"asexual"
] | A | sexual | The lifecycle of basidiomycetes includes alternation of generations (Figure 24.16). Spores are generally produced through sexual reproduction, rather than asexual reproduction. The club-shaped basidium carries spores called basidiospores. In the basidium, nuclei of two different mating strains fuse (karyogamy), giving rise to a diploid zygote that then undergoes meiosis. The haploid nuclei migrate into basidiospores, which germinate and generate monokaryotic hyphae. The mycelium that results is called a primary mycelium. Mycelia of different mating strains can combine and produce a secondary mycelium that contains haploid nuclei of two different mating strains. This is the dikaryotic stage of the basidiomyces lifecyle and and it is the dominant stage. Eventually, the secondary mycelium generates a basidiocarp, which is a fruiting body that protrudes from the ground—this is what we think of as a mushroom. The basidiocarp bears the developing basidia on the gills under its cap. | science |
The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 400 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 5 units? | [
"40 sq.units",
"158 sq.units",
"187 sq.units",
"607 sq.units"
] | A | 40 sq.units | Given that the area of the square = 400 sq.units
=> Side of square = √400= 20 units
The radius of the circle = side of the square = 20 units
Length of the rectangle = 2/5 * 20 = 8 units
Given that breadth = 5 units
Area of the rectangle = lb = 8 * 5 = 40 sq.units
Answer: A | aqua_rat |
Average score for Virat Kohli in a series of 10 matches is 38.9 runs. If the average for first six matches comes out to be 42 what is his average in the last 4 matches of the series? | [
"34.25",
"35",
"33.25",
"34.25"
] | A | 34.25 | Explanation:
Average runs scored by Virat Kohli in 10 matches: Total runs scored/10—(1)
Average runs scored by Virat Kohli in 6 matches: (Total runs in 6 matches)/6
=> 42 = Runs/6
=>252 runs
Using (1):
=>38.9 = Runs/10
=>389 runs
Runs scored in rest 4 matches: 389 - 252 runs
=> 137 runs
Average runs scored by Virat Kohli in 4 matches: 137/4 = 34.25 runs
ANSWER A | aqua_rat |
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.10 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? | [
"160",
"175",
"190",
"200"
] | C | 190 | Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.10 + X x 3.20 = 432
X = 30.
Hence, total hours of work = (160 + 30) = 190.
answer :C | aqua_rat |
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : | [
"Rs. 110.75",
"Rs. 115.75",
"Rs. 124.75",
"Rs. 125"
] | C | Rs. 124.75 | For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C | aqua_rat |
If milk is going to be measured, it can be measured in | [
"only a thin tube",
"only a round dish",
"any kind of shape container",
"only a square container"
] | C | any kind of shape container | science | |
An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 10, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold? | [
"a.\tA - 10",
"b.\tB - 15",
"c.\tC – 22.5",
"d.\tD – 20"
] | D | d. D – 20 | A --- 30/2 + 10 = 25 --- wrong
B --- 45/2 + 10 = not an integer --- wrong
C --- 22.5(3/2) + 10 = not an integer --- wrong
D --- 60/2+10 = 40 --- CORRECT
This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.
D | aqua_rat |
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