divelab/Sys2Bench huggingface dataset:
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 5^a and y = 7^b, which of the following is a possible units digit of xy?
Options:
A)1
B)4
C)5
D)7
E)8
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=5
a=2; X=25
a=3; X=125........ Units digit repeat in a cycle of 5......
Similarly, Finding all values ofYfor positive values ofb
When,
b=1; Y=7
b=2; Y= 49
b=3; Y= 343
b=4; Y=2041
b=5; Y=16807....... Units digit repeat in cycle of 7,9,3,1,7,9,3....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=5 and Y=7: Units digit of XY = 35
When X=5 and Y=9: Units digit of XY = 45
When X=5 and Y=3: Units digit of XY = 15
When X=5 and Y=1: Units digit of XY = 5
Only one possibilities for Units digit of XY i.e. 5
therefore answer is C
Answer: C
Question: Using all the letters of the word "FRIDAY", how many different words can be formed?
Options:
A)A)7
B)B)8!
C)C)8
D)D)7!
E)E)5!
Rationale: Explanation:
Total number of letters = 5
Using these letters the number of 5 letters words formed is 5!.
Answer: Option E
Answer: E
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 522.416 is divided by 0.0168?
Options:
A)5
B)6
C)4
D)3
E)7
Rationale: for the 1st no. there are 3 digits after decimal
for the 2nd no. there are 5 digits after decimal
total no. of decimals = 8
req. no. of digits=(n-1)=(8-1)=7
ANSWER :E
Answer: E
Question: The average monthly salary of laborers and supervisors in a factory is Rs.1250 per month; where as the average monthly salary of 6 supervisors is Rs.2450. If the average monthly salary of the laborers is Rs.850 find the number of laborers?
Options:
A)14
B)15
C)16
D)17
E)18
Rationale: 2450 850
\ /
1250
/ \
400 1200
1:3
1-->6
3-->?
18
ANSWER:E
Answer: E
Question: There is a road beside a river.Two friends started from a place A, moved to a temple situated at another place B and then returned to A again. One of them moves on a cycle at a speed of 12 km/hr, while the other sails on a boat at a speed of 10 km/hr. If the river flows at the speed of 4 km/hr, which of the two friends will return to place A first ?
Options:
A)5.4 km /hr
B)7.2 km /hr
C)8.4 km/hr
D)9.6 km /hr
E)4.6 km /hr
Rationale: speed of cycle both side on road will be same
average speed of cycle = 12 kmhr
downstream , boat speed =10+4= 14kmhr
upstream = 10- 4 = 6kmhr
averge of boat speeds =( 2* 14* 6)/14+6=8.4 kmhr
ANSWER:C
Answer: C
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)187 m
B)278 m
C)279 m
D)270 m
E)872 m
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: D
Question: Find the odd man out. 1050, 510, 242, 106, 46, 16, 3
Options:
A)46
B)106
C)510
D)1050
E)16
Rationale: Explanation :
1050
(1050 - 30)/2 = 510
(510 - 26)/2 = 242
(242 - 22)/2 = 110
(110 - 18)/2 = 46
(46- 14)/2 = 16
(16- 10)/2 = 3
Hence, 110 should have come in place of 106
Answer : Option B
Answer: B
Question: If the area of circle is 616 sq cm then its circumference?
Options:
A)11
B)88
C)99
D)266
E)12
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88 Answer: B
Answer: B
Question: ((1^(m+1))/(5^(m+1)))((1^18)/(4^18)) = 1/(2(10)^35)
What is m?
Options:
A)17
B)18
C)34
D)35
E)36
Rationale: ((1^(m+1))/(5^(m+1)))((1^18)/(4^18)) = 1/(2(10)^35)
((1/5)^(m+1) ) * ((1/2)^36) = 1/ (2 * (2*5)^35))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^(m+1)= (1/5)^35
((1/5)^(m+1) ) * ((1/2)^36) = 1/[(2^36)*(5^35)]
So, m=34
Answer C
Answer: C
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age
of all
Options:
A)15.5
B)15
C)16
D)Cant be computed
E)None of these
Rationale: Explanation:
As number of girls and boys is not given so result cant be computed
Answer: Option D
Answer: D
Question: Find the simple interest on Rs.567 for 7 months at 9 paisa per month?
Options:
A)s.357.21
B)s.322.12
C)s.400
D)s.278.9
E)s.300
Rationale: Explanation:
I = (567*7*9)/100 = 357.21
Answer: Option A
Answer: A
Question: Look at this series: 97, 97, 93, 93, 89, 89, 85, 85, ... What number should come next?
Options:
A)75
B)76
C)78
D)81
E)80
Rationale: Explanation:
In this series, each number is repeated, then 4 is subtracted to arrive at the next number.
Answer: Option D
Answer: D
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/3 of the remaining paint. How many gallons of paint has Joe used?
Options:
A)18
B)180
C)175
D)216
E)250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/4)*360 = 90 gallons.
Remaning paint = 270 gallons
Paint used in the second week = (1/3)*270 = 90 gallons
Total paint used = 180 gallons.
Option B
Answer: B
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: C99, F102, __, L108, O111, ... What number should fill the blank?
Options:
A)I105
B)J106
C)K107
D)L109
E)M110
Rationale: A
I105
In this series, the letters progress by 3, and the numbers increase by 3.
Answer: A
Question: Which of the following numbers is between 1⁄3 and 2⁄5?
Options:
A).45
B).35
C).29
D).22
E).20
Rationale: 1/3 = .333...
2/5 = .4
The only number between these two is 0.35.
The answer is B.
Answer: B
Question: The average of 10 numbers is calculated as 18. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)A)16
B)B)18
C)C)19
D)D)22
E)E)24
Rationale: Explanation:
10 * 18 + 36 – 26 = 190=>190/10 = 19
C)
Answer: C
Question: A coin is weighted so that the probability of heads on any flip is 0.2, while the probability of tails is 0.8. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?
Options:
A)(0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2
B)(0.3)^5 + 4(0.3)^4(0.8) + 6(0.3)^3(0.8)^2
C)(0.3)^5 + 3(0.3)^4(0.8) + 2(0.3)^3(0.8)^2
D)(0.3)^5 + 2(0.3)^4(0.8) + (0.3)^3(0.8)^2
E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2
Rationale: Probability of Head, P(H) = 0.2
Probability of Tail, P(T) = 0.8
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.2)^3*(0.8)^2
1 Tail and 4 Heads, Probability = 5C1*(0.2)^4*(0.8)^2
0 Tail and 5 Heads, Probability = (0.2)^5
Required Probability = Sum of all Favourable cases = (0.2)^5 + 5(0.2)^4(0.8) + 10(0.2)^3(0.8)^2
Answer: option A
Answer: A
Question: If circles x and y have the same area and circle x has a circumference of 14π, half of the radius of circle y is:
Options:
A)16
B)8
C)4
D)3.5
E)1
Rationale: x be radius of circle x
y be radius of circle y
given:
pi*x^2 = pi*y^2
also,
2*pi*x = 14*pi
x =7
thus y =7
y/2 = 3.5
Ans: D
Answer: D
Question: If n is an integer number, and m=115n, then m must be divisible by which of the following?
Options:
A)11
B)15
C)23
D)25
E)230
Rationale: m=115n
m=5∗23n
So, m must be divisible by 5 & 23 both...
Among the given options only (C) satisfies.
Answer: C
Question: Ram draws a card randomly among card 1-23 and keep it back. Then Sam draws a card among those. What is the probability that Sam has drawn a card greater than ram.
Options:
A)11/27
B)11/24
C)11/23
D)11/21
E)11/22
Rationale: If Ram draws 1, then Sam can draw anything from 2 to 23 = 22 ways
If Ram draws 2, then Sam can draw anything from 3 to 23 = 21 ways
. . . .
. . . .
If Ram draws 23, Sam has no option = 0 ways.
Total required ways = 22 + 21 + 20 + . . . . + 0 = 22×23222×232 = 253
Total ways of drawing two cards = 23×23
Required probability = 253/529=11/23
Answer:C
Answer: C
Question: 3.5 can be expressed in terms of percentage as?
Options:
A)0.35%
B)3.5%
C)35%
D)350%
E)NONE
Rationale: 3.5 = 35/10 = (35/10 * 100) = 350%
ANSWER:D
Answer: D
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)1/121
B)1/213
C)1/216
D)2/211
E)3/213
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)2878
B)277
C)245
D)299
E)271
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.Answer: C
Answer: C
Question: Tom can hit a target 3 times in 6 shots, Marry can hit the target 2 times in 6 shots & mike can hit 4 times in 4 shots. What is the probability that atleast 2shots hit the target ?
Options:
A)3/4
B)4/5
C)2/3
D)5/7
E)6/8
Rationale: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: C
Question: A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68m/min. The area of the field is?
Options:
A)33
B)60
C)88
D)27
E)26
Rationale: Explanation:
length of the diagonal = 52*(15/60) =13m
sum of length and breadth = 68*(15/60) = 17m
\inline {\color{Black}\sqrt{l^{2}+b^{2}}=13 \; or\; l+b=17 }
area =lb = 1/2[(2lb)] = 1/2[(l+b)² - (l²+b²)] = 1/2[17² -169]
=1/2*120 = 60 sq meter
Answer: B) 60
Answer: B
Question: 3,14,39,_?
Options:
A)81
B)82
C)83
D)84
E)85
Rationale: n^3 + n^2 + n
Soln : 1^3+1^2+1 = 3
2^3+2^2+2 = 8+4+2 = 14
3^3+3^2+3 = 27+9+3 = 39
4^3+4^2+4 = 64+16+4 = 84
ANSWER:D
Answer: D
Question: The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 81. What is the difference between the two digits of that number?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Sol.
Let the ten’s digit be x and unit’s digit be y,
Then, (10x + y) - (10y + x) = 81 ⇔ 9 (x - y) = 81
⇔ x - y = 9
Answer E
Answer: E
Question: In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/6 . If the probability that a number 12 or larger is drawn is 1/2 , what is the probability that a number less than or equal to 20 is drawn?
Options:
A) 1/18
B) 1/6
C) 2/3
D) 1/2
E) 5/6
Rationale: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 12 or larger
Set 2: Number 20 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)
1/2 + P(Set 2) - 1/6 = 2/3
P(Set 2) = 2/3
Answer (C)
Answer: C
Question: In how many ways can the word DAILY arranged?
Options:
A)720
B)100
C)620
D)120
E)150
Rationale: DAILY-there are 5 letters.
so we have 5 possible arrangements.
5!=5*4*3*2*1=120 was
Answer is option D
Answer: D
Question: The value of x + x(xx) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Options:
A)10
B)2
C)8
D)6
E)4
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer is A.
Answer: A
Question: A cylinder of height h is 6/7 of water. When all of the water is poured into an empty cylinder whose radius is 25 percent larger than that of the original cylinder, the new cylinder is 3/5 full. The height of the new cylinder is what percent of h?
Options:
A)25%
B)50%
C)60%
D)70%
E)100%
Rationale: Basically we can disregard the radius is 25% information, as we are only asked about the height of the original and the new cylinder.
This is becausethe new cylinder is 3/5 fullmeans the same as that it's height is 3/5.
Original cylinder 6/7
New cylinder 3/5
So 3/5/6/7 = 3/5*7/6= 0.70 or 70%.
Answer D
Answer: D
Question: There is a 55 cm line marked at each centimeter and an insect is placed at every centimeter. 9 frogs are trained to jump a constant distance. The first one jumps 2 cm in every leap, the second one jumps 3 cm and so on until the 9th one jumps 10 cm in every leap and they eat any insect that is available at that spot. If all of them start from start line and finish the entire 55 cm, how many insects were still left after the race was over?
Options:
A)0
B)3
C)6
D)9
E)12
Rationale: Only the prime numbers greater than 10 and less than 55 were left.
That is 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and 53.
The total is 12.
The answer is E.
Answer: E
Question: A certain sum of money at simple interest amounted Rs.1240 in 6 years at 4% per annum, find the sum?
Options:
A)998
B)1000
C)890
D)646
E)789
Rationale: 1240 = P [1 + (6*4)/100]
P = 1000
Answer: B
Answer: B
Question: If -0.5 < x < 0, which of the following must be true?
I. x^7 < x^2
II. x^3 < 1 – x^3
III. x^4 < x^2
Options:
A)I only
B)I and II only
C)II and III only
D)I and III only
E)I, II and III
Rationale: I. x^7 < x^2 --> from -0.5 < x < 0 it follows that LHS<0<RHS, so this statement is true.
II. x^3 < 1 – x^3 --> x^3(1+1) < 1 --> negative*positive < 0 < 1, so this statement is also true.
III. x^6 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 0 is follows that x^4>0): x^4 < 1. Again, as -1 < x < 0, then x^4 must be less than 1. Hence, this statement is also true.
Answer: E.
Answer: E
Question: An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
Options:
A)2200 kmph
B)1800 kmph
C)1900 kmph
D)2100 kmph
E)none
Rationale: Explanation: Distance = (1500 x 2) = 3000 km.
Speed = Distance/Time
Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = 3000 x 3/5 km/hr = 1800 km/hr.
Answer: Option B
Answer: B
Question: The total weight of six people of equal weights inside a car is 12% of the total weight of the car (inclusive of the six people inside). If three people get down from the car, what will be the ratio of the weight of people inside the car to the weight of the empty car?
Options:
A)44
B)45
C)46
D)47
E)48
Rationale: Ans. Assume total weight of the car along with people is 100kgs.
Then Total weight of 6 people is 12% of 100 = 12 kgs. So empty car weight = 88 kgs
That is, the weight of a single person = 12/6 = 2 kgs.
If three people get down from the car, then there is a six kgs reduction in the total weight and the weight of the remaining people is only 6 kgs.
The required ratio = 6 : 88 = 3 : 44
Answer A
Answer: A
Question: If the cost price of 12 pens is equal to the selling price of 7 pens, the gain percent is:
Options:
A)80%
B)90%
C)71%
D)40%
E)10%
Rationale: Explanation:
Let C.P. of each pen be Re. 1.
Then, C.P. of 7 pens = Rs. 7; S.P. of 7 pens = Rs. 12.
Gain % = 5/7 * 100 = 71%
Answer:C
Answer: C
Question: John would make the 3-letter codes with 26 alphabets in condition that the middle letter must be vowel and the first letter and the third letter must be different from each other and both are consonant. How many cases of the codes are there?
Options:
A)1,980
B)2,020
C)2,100
D)2,200
E)2,500
Rationale: No of Vowels: 5 (A, E, I ,O ,U)
No of Consonants: 21 (26-5)
Now,
The Middle letter can be filled up in 5 ways.
The First letter can be filled in 21 ways ( As only consonants are allowed)
As one of the consonants is used in the first letter, the third letter can be filled up in 20 ways, so that the letter must be different from each other.
So total number of ways = 21 x 5 x 20 = 2100
Answer: C
Answer: C
Question: The sum of the two numbers is 15 and their product is 35. What is the sum of the reciprocals of these numbers?
Options:
A)15/35
B)1/35
C)35/8
D)7/32
E)None of these
Rationale: Let the numbers be a and b. Then, a+b=15 and ab =35.
a+b/ab=15/35; (1/b+1/a)=15/35
Sum of reciprocals of given numbers=15/35.
Correct Option: A
Answer: A
Question: Of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout, the number of males is 45 more than twice the number of females. If the ratio of female speckled trout to male rainbow trout is 4:3 and the ratio of male rainbow trout to all trout is 3:20, how many female rainbow trout are there?
Options:
A)192
B)195
C)200
D)205
E)208
Rationale: It will be easier if you draw a table for this one. Let T be the total trout.
total speckled trout (ST) = 645
If female speckled trout = fST
then male speckled trout = 45 + 2fST
Therefore 45+ 2fST + fST = 645
We solve and get fST = 200
and mST= 445
Ratio of fST to mRT = 4:3
We have fST = 200
Solve ratio to get mRT = 150
Now ratio of mRT to T = 3:20
We have mRT = 150
Solve ratio to get T = 1000
Now unless youve drawn the table it might get a little complex.
From above we have mST and mRT
mST + mRT = 445 + 150 = 595
So T - 595 = total female trouts
1000 - 595 = 405 female trouts
We have from above that fST = 200
So (whew!) fRT = 405 - 200 = 205 answer is D
Answer: D
Question: There are 16 bees in the hive , then 7 more fly. How many bees are there in all?
Options:
A)7
B)23
C)12
D)17
E)25
Rationale: 16+7=23 . Answer is B.
Answer: B
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
Options:
A)Rs.1500
B)Rs.1300
C)Rs.1200
D)Rs.1000
E)Rs.1700
Rationale: Explanation:
(x*5*1)/100 + [(2500 - x)*6*1]/100 = 140
X = 1000
ANSWER IS D
Answer: D
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
Options:
A)1/8
B)1/2
C)4/2
D)1/9
E)7/2
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then
= 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
Answer: B
Question: Two taps A and B can fill a cistern in 12 minutes and 18 minutes respectively. They are turned on at the same time. If the tap A is turned off after 4 minutes, how long will tap B take to fill the rest of the cistern ?
Options:
A)8 minute
B)9 min.
C)10 min.
D)7 min.
E)None of these
Rationale: In one min, (A + B) fill the cistern = 1⁄12 + 1⁄18 = 5⁄36th
In 4 min, (A + B) fill the cistern = 5⁄36 × 4 = 5⁄9th
Rest part = 1 - 5⁄9 = 4⁄9th
∵ 1⁄18th part is filled by B in one min.
∴ 4⁄9th part is filled by B in 18 × 4⁄9 = 8 min
Answer A
Answer: A
Question: IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT
Options:
A)a) 3x^3
B)b)x (x+3)
C)c)9 x^2
D)d)3 x^7
E)e)x(x+1)(x+2)
Rationale: *any number multiplied by 3, will be divided by 3
for option b if we put value x=7, 7*10=70 is not divisible by 3
Answer : B
Answer: B
Question: Jordan passed a point on a track at a constant speed of 50 miles per hour. Then, 15 minutes later, Pauline passed the same point at a constant speed of 60 miles per hour. If both runners maintained their speeds , how long after he passed the gas station did Pauline catch up with Jordan?
Options:
A)30 min
B)45 min
C)1 hr
D)1 hr 15 min
E)1 hr 30 min
Rationale: When Pauline is at the point, Jordan is 50/4 miles ahead on the ahead. (the distance covered by him in 15 min)
every hour, pauline runs 10 miles more than Mary. how many hours will it takes him to run 50/4 miles more? the answer is (50/4)/10 = 25/20=1h15min.
Answer D
Answer: D
Question: If two girls starting from same point, walking in the opposite directions with 7km/hr and 3km/hr as average speeds respectively. Then the distance between them after 12 hours is?
Options:
A)120
B)121
C)122
D)123
E)124
Rationale: Explanation:
Total distance = Distance traveled by person A+ Distance traveled by person B
= (7Ã— 12) + (3Ã— 12)
= 84+ 36
= 120 Km
Answer:A
Answer: A
Question: Perimeter of the backwheel is 9 feet and front wheel is 7 feet at a certain distance. The front wheel gets 10 revolutions more than the back wheel. What is the distance?
Options:
A)305
B)310
C)315
D)320
E)325
Rationale: If distance=d
Number of revolutions by back wheel=d/9 & front wheel=d/7
(d/7)-(d/9)=10 ,2d=630 ,d=315
ANSWER:C
Answer: C
Question: You have 59 cubic blocks. What is the minimum number that needs to be taken away in order to construct a solid cube with none left over?
Options:
A)28
B)29
C)30
D)31
E)32
Rationale: Sol.
The next cube number below 64(4 ×4 ×4) is 27(3 ×3 ×3).
In order to construct a solid cube, therefore, with none left over,
59 – 27 = 32 blocks need to be taken away.
Answer : E
Answer: E
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $3,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
Options:
A) 15,500
B) 24,500
C) 25,500
D) 26,500
E) 27,500
Rationale: OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 3,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 3,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 240 = 0.10x
Combine terms and subtract 0.08x from both sides:
310 = 0.02x
Divide both sides by 0.02:
15,500 = x
Your answer is A.
Answer: A
Question: In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race?
Options:
A)167 sec
B)190 sec
C)176 sec
D)716 sec
E)615 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/16 = 625 sec.
Time taken by A = 625 - 10
= 615 sec.
Answer:E
Answer: E
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
Options:
A)10
B)11
C)12
D)16
E)21
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: C
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
Options:
A)104 kmph
B)776 kmph
C)886 kmph
D)887 kmph
E)665 kmph
Rationale: 624/6 = 104 kmph
Answer: A
Answer: A
Question: The area of one square is x^2 + 4x + 4and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?
Options:
A)0
B)2
C)2.5
D)4.67
E)3
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+2)^2A2= (2x-3)^2
L1= x+2L2= 2x-3
P1 = 4( x+2)P2=4(2x-3)
P1+P2=32
4( x+2) +4(2x-3)=32..............> X=3
Answer: E
Answer: E
Question: If (8x)/(11y/z -1) = 3x then which of the following is true?
Options:
A)z = -3y
B)z = -y
C)z = -x
D)z = 3y
E)z = 3x
Rationale: (8x)/(11y/z - 1) = 3x
=> 8z/(11y - z) = 3
=> 8z = 33y - 3z
=> 11z = 33y
=> z = 3y
Hence Ans is D
Answer: D
Question: Which of the following could be the sides of an obtuse angled triangle? all values are degree only
I. 51, 29, 100
II. 32, 33,4 4
III. 52, 53, 55
Options:
A)I and III only
B)I only
C)III only
D)I and II only
E)I, II and III
Rationale: obtuse angled triangle means one angle more than 90deg and total 180 deg.. I
HENCE, (B)
Answer: B