divelab/Sys2Bench huggingface dataset:
Question: The cost of an article is decreased by 20%. If the original cost is $120, find the decrease cost.
Options:
A)33
B)11
C)96
D)36
E)91
Rationale: Original cost = $120
Decrease in it = 20% of $120
= 20/100 Ã— 120
= 2400/100
= $24
Therefore, decrease cost = $120 - $24 = $96
Answer:C
Answer: C
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 12 years and that of the other 9 students is 16 years. The age of the 15th student is?
Options:
A)11 years
B)17 years
C)21 years
D)14 years
E)12 years
Rationale: Age of the 15th student
=[15 * 15 - (12 * 5 + 16 * 9)]
= (225 - 204)
= 21 years.
Answer:C
Answer: C
Question: 2 gears one with 12 teeth and other one with 15 teeth are engaged with each other. One teeth in smaller and one tooth in bigger are marked and initially those 2 marked teeth are in contact with each other. After how many rotations of the smaller gear with the marked teeth in the other gear will again come into contact for the first time?
Options:
A)5
B)12
C)48
D)60
E)120
Rationale: Assume that the distance b/w gears be 1cm.
Then the circumference of 1st gear is 12cm and 2nd gear is 15cm.
So.
The LCM of 12 and 15 is 60.
So,
1st gear has rotate 60/12=5(Smaller Gear)
2nd gear has rotate 60/15=4(Bigger Gear)
So,
The answer is 5.
ANSWER:A
Answer: A
Question: The radius of a cylinder is 9 m, height 12 m. The volume of the cylinder is:
Options:
A)2200
B)5500
C)3054.9
D)1100
E)4400
Rationale: Cylinder volume = Ï€r(power2)h
= 22/7 Ã— 9 Ã— 9 Ã— 12
= 3054.9 m(power3)
Answer is C.
Answer: C
Question: A baseball team won 40 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
Options:
A)36
B)45
C)49
D)55
E)81
Rationale: Games won out of first 80 questions = (40/100)*80 = 32
Total Games = 80+82 = 162
Games to be won = (50/100)*162 = 81
Remaining games to be won = 81-32 = 49
Answer: Option C
Answer: C
Question: If there are 9 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
Options:
A)632
B)672
C)756
D)744
E)740
Rationale: Firstly, there are 9 ways to choose 3 groups from the 4 groups. Hence 9C3.
Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.
Hence, the total number of ways are 9C3 * (2^3) = 672
B
Answer: B
Question: One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 14 percent sugar by weight. The second solution was what percent sugar by weight?
Options:
A)74%
B)64%
C)42%
D)28%
E)26%
Rationale: Say the second solution (which was 1/4 th of total) was x% sugar, then 3/4*0.1+1/4*x=1*0.14 --> x=0.26. Alternately you can consider total solution to be 100 liters and in this case you'll have: 75*0.1+25*x=100*0.14 --> x=0.26.
Answer: E.
Answer: E
Question: A number x is multiplied by 7, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x if x≠0 ?
Options:
A)25/9
B)7/3
C)5/3
D)3/5
E)9/25
Rationale: sqrt(7x/3) to be perfect square x has to 7/3
Ans: B
Answer: B
Question: If 4 boys can color 48 m long cloth in 2 days, then 6 boys can color 36 m long cloth in
Options:
A)1 day
B)2 days
C)3 days
D)4 days
E)5 days
Rationale: The length of cloth painted by one boy in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 boys = 36/ 6 × 6 = 1 day.
A)
Answer: A
Question: 7, 10, 8, 11, 9, 12, ___
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: 10= 7+3
8 = 10-2
11= 8+3
9 = 11-2
12 =9+3
Similarly 12-2=10
ANSWER:A
Answer: A
Question: If a sum of money doubles itself in 25 years at simple interest, the ratepercent per annum is
Options:
A)12
B)12.5
C)13
D)13.5
E)4
Rationale: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 25) = 4
Option E
Answer: E
Question: In Hockey game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
Options:
A)1/3
B)4/9
C)5/9
D)2/3
E)3/4
Rationale: In Hockey game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.
Answer: C.
Answer: C
Question: A bowl contains equal numbers of red, orange, green, blue, and yellow candies. Kaz eats all of the green candies and half of the orange ones. Next, he eats half of the remaining pieces of each color. Finally, he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 20% of the original number. What percent of the red candies remain?
Options:
A)5%
B)7.5%
C)10%
D)12.5%
E)15%
Rationale: Let x be the original number of each color.
Kaz eats all of the green candies and half of the orange ones.
There are 0 green candies and 0.5x orange candies remaining.
He eats half of the remaining pieces of each color.
There are 0.25x orange candies, and 0.5x each of red, yellow, and blue candies.
He eats red and yellow candies in equal proportions.
orange+blue+red+yellow = 0.75x + red + yellow = x
red + yellow = 0.25x
red = 0.125x, since red = yellow.
The answer is D.
Answer: D
Question: Find the perimetri of trapezium with sides 4,6,12 and distance between two parallel side is 3.
Options:
A)27
B)26
C)28
D)25
E)24
Rationale: 1/2*(6+12)*3=27
ANSWER:A
Answer: A
Question: A gardener wants to plant trees in his garden in rows in such away that the number of trees in each row to be the same. If there are 24 rows the number of trees in each row is 42 if there are 12 more rows find the number of trees in each row?
Options:
A)21
B)28
C)34
D)32
E)76
Rationale: Required number of trees
= 24/36 * 42 = 28.
Answer:B
Answer: B
Question: Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly
Options:
A)Rs 2520
B)Rs 2521
C)Rs 2522
D)Rs 2523
E)None of these
Rationale: Explanation:
Please remember, when we have to calculate C.I. quarterly then we apply following formula if n is the number of years
Amount=P(1+R/4 /100)4n
Principal	= Rs.16,000;
Time=9 months	= 3 quarters;
Rate = 20%, it will be 20/4 = 5%
So lets solve this question now,
Amount=16000(1+5/100)3=18522
C.I=18522−16000=2522
Option C
Answer: C
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options:
A)900 sq.cm.
B)700 sq.cm.
C)800 sq.cm.
D)400 sq.cm.
E)600 sq.cm.
Rationale: Explanation:
Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer: Option E
Answer: E
Question: In the coordinate plane, the points F (-1,1), G (1,3), and H (3,1) lie on a circle with center P. What are the coordinates of point P ?
Options:
A)(0,0)
B)(1,1)
C)(1,2)
D)(1,-2)
E)(2.5, -2.5)
Rationale: I thought I need to find the 4th point that would lie on the circle
Hence my answer was D (1,-1)
But the the center of the circle will lie on (1,1)
Answer: B
Question: A man rows to a place 48 Km distance and back in 14 hours. He finds that he can row 4 Km with the stream in the same time 3 Km against the stream. The rate off the stream is?
Options:
A)5
B)3
C)2
D)1
E)4
Rationale: Let be moves 4km downstream in X Hours
Then in speed downstream = Kmph
Speed in upstream = 4/X Kmph
==> 48/4/X + 48/3/X = 14
==> 12X + 16X =14
==> X = 1/2
Speed in downstream = 8 Kmph
Speed in up stream = 6 Kmph
Then the Rate of stream = 1/2 (8 - 6) = 1 Kmph
Answer is D.
Answer: D
Question: If a(a + 8) = 9 and b(b + 8) = 9, where a ≠ b, then a + b =
Options:
A) −8
B) −2
C) 2
D) 46
E) 48
Rationale: a(a + 8) = 9
=> we have a = 1 or -9
also b(b + 8) = 9
=> b = 1 or -9
given a ≠ b
1) when a =1, b= -9 and a + b = -8
1) when a = -9, b= 1 and a + b = -8
Answer choice A
Answer: A
Question: A man took a loan from a bank at the rate of 10% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :
Options:
A)Rs. 2000
B)Rs. 10,000
C)Rs. 18,000
D)Rs. 20,000
E)None
Rationale: Solution
Principal = Rs.(100x5400/10x3)= Rs. 18000.
Answer C
Answer: C
Question: The speed of a boat in upstream is 100 kmph and the speed of the boat downstream is 170 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)17 kmph
C)19 kmph
D)35 kmph
E)29 kmph
Rationale: Speed of the boat in still water
= (100+170)/2
= 135 kmph. Speed of the stream
= (170-100)/2
=35kmph.
Answer: D
Answer: D
Question: If the average (arithmetic mean) of x + 3, x + 4, and x + 5 is 0, then x =
Options:
A)–4
B)–3
C)–2
D)–1
E)0
Rationale: (x+3 + x+4 + x+5)/3 = 0
=>3x + 12 = 0
=>x = -4
Answer A
Answer: A
Question: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 -9/20=
Options:
A)0
B)2/15
C)2/5
D)9/20
E)5/6
Rationale: We need to determine the result of 1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20
Let’s add the given fractions in two groups. In the group of the first three fractions, notice that1/3 and 1/2 share a common denominator of 6 with 5/6.
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Thus, 5/6 – 5/6 = 0
Looking at the 2nd group of the fractions (1/5, 1/4, and 9/20), notice that1/5 and 1/4 share a common denominator of 20 with 9/20.
1/5 + 1/4 = 4/20 + 5/20 = 9/20
Thus, 9/20 – 9/20 = 0.
Thus, the result of 1/3 + 1/2 – 5/6 + 1/5 + 1/4 – 9/20 is 9/20.
Answer: D
Answer: D
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 277830, then population in 1978 was?
Options:
A)120000
B)120029
C)187899
D)178968
E)240000
Rationale: X * (105/100) * (105/100) * (105/100) = 277830
X = 277830/1.157625
X = 240000
Answer:E
Answer: E
Question: There is an unlimited stock of blue, red, white, and grey coloured balls. What is the number of ways of selecting 12 balls from the stocks?
Options:
A)735
B)445
C)455
D)475
E)854
Rationale: Let us say that we have selected 'x1' blue balls, 'x2' red balls, 'x3' white balls and 'x4' grey coloured balls.
This means, x1+x2+x3+x4 = 12
Now, for an intance, 1+2+3+6 can be an answer. 0+0+0+12 can also be another answer
Hence, we need to find the non-negative integral solution for the equation
x1+x2+x3+x4 = n is
(n+k-1)C(k-1)
Here, n=12 and k=4
(12+4-1)C(4-1) = 15C3 = 455
ANSWER:C
Answer: C
Question: There are 4 more women than there are men on a local co-ed softball team. If there are a total of 20 players on the team, what is the ratio of men to women?
Options:
A)10/16
B)6/16
C)4/16
D)6/10
E)8/12
Rationale: w = m+4
w+m = 20
m+4+m = 20
2m = 16
m = 8
w = 12
ratio:8:12
Ans: E
Answer: E
Question: The vertex of a rectangle are (1, 0), (5, 0), (1, 2) and (5, 2) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
Options:
A)3
B)6
C)1/3
D)1/2
E)1/6
Rationale: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (3, 1). The slope of a line passing through (0,0) and (3, 1) is 1/3.
The answer is C.
Answer: C
Question: The value of land increases by r% during June and decreases by s% during July. If the value of the land is the same at the end of July as at the beginning of June, what is s in terms of r?
Options:
A)200r/(100+2r)
B)100r/(100+r)
C)r(2+r)/(1+r)2
D)r(200+r)/10000
E)2r/r+2r
Rationale: The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
ans B
Answer: B
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 19.36, the number of the member is the group is:
Options:
A)57
B)67
C)77
D)87
E)44
Rationale: Money collected = (19.36 x 100) paise = 1936 paise.
Number of members =Square root of 1936 = 44
Answer: Option E
Answer: E
Question: Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 54,000 after completion of one year. What will be Madhu's share of profit?
Options:
A)Rs. 27,000
B)Rs. 24,000
C)Rs. 30,000
D)Rs. 36,000
E)None of these
Rationale: 30,000 *12=45,000*8
1:1
Madhu's share=1/2*54,000
i.e. Rs. 27,000
ANSWER:A
Answer: A
Question: If â€˜MANIPURâ€™ is coded as â€˜DAEIGCI', then â€˜MIZORAMâ€™ is coded as
Options:
A)DDFIHIA
B)HIADDFI
C)DFIHIAD
D)DHIFIAD
E)DIHFIAD
Rationale: M=13,1+3=4=D
A=1=A
SIMILARLY,
M=13=1+3=4=D
I=9=I
Z=26=2+6=8=H
O=15=1+5=6=F
R=18=1+8=9=I
A=1=A
M=13=1+3=4=D
SO ANS IS
DIHFIAD
ANSWER:E
Answer: E
Question: Jack purchased two chairs at a discount of 50%. Sally purchased a table at a discount of 80%. Jack spent more on his two chairs than Sally did on her table. If Jack had purchased his two chairs at a discount of 60%, he would have spent less than Sally. If z represents the undiscounted price of Sally's table, which of the following could be the average undiscounted price of Jack's two chairs, in terms of z?
Options:
A)0.25z
B)0.22z
C)0.19z
D)0.15z
E)0.13z
Rationale: Let the average undiscounted price of Jack's two chairs be x, so 2 undiscounted chairs cost 2x.
Jack purchased two chairs at a discount of 50% --> he paid 0.5*2x = x.
Sally purchased a table at a discount of 80% --> she paid 0.2z.
Jack spent more on his two chairs than Sally did on her table --> x > 0.2z. Eliminate options C, D and E.
If Jack had purchased his two chairs at a discount of 60%, so for 0.4*2x = 0.8x, he would have spent less than Sally --> 0.8x < 0.2z --> x < 0.25z. Eliminate A.
Answer: B.
Answer: B
Question: In measuring the sides of a rectangle, one side is taken 5% in excess and the other 4% in deficit. Find the error percent in the area, calculate from the those measurements.
Options:
A)0.9%
B)0.8%
C)0.3%
D)0.2%
E)0.5%
Rationale: Explanation:
let x and y be the sides of the rectangle then
correct area =
=
Error% =
Answer: B) 0.8%
Answer: B
Question: The ratio of the earnings of P and Q is 9 : 10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
Options:
A)3/9
B)3/2
C)3/5
D)3/6
E)3/1
Rationale: Let the earnings of P and Q be Rs. 9x and Rs. 10x respectively.
New ration = [9x + 1/4(9x)]/[10x - 1/4(10x)]
=> [9x(1 + 1/4)]/[10x(1 - 1/4)]
= 9/10 * (5/4)/(3/4) => 3/2.
Answer:B
Answer: B
Question: When x is divided by 2, the quotient is y and the remainder is 1. When x is divided by 5, the quotient is z and the remainder is 6. Which of the following is the value of y in terms of z?
Options:
A)4z/7 + 5
B)(7z + 5) / 6
C)(6z + 7) / 4
D)(5z + 5) / 2
E)(4z + 6) / 7
Rationale: When x is divided by 2, the quotient is y and the remainder is 1: x = 2y + 1.
When x is divided by 5, the quotient is z and the remainder is 6: x = 5z + 6.
Equate those two:
2y + 1 = 5z + 6;
y = (5z + 5)/2.
Answer: D.
Answer: D
Question: A lighting store is stocked with 410 fixtures. Some of the fixtures are floor lamps and the rest are table lamps. If 5% of the floor lamps and 30% of the table lamps are imported, what is the smallest possible number R of imported lamps stocked at the store?
Options:
A)3
B)10
C)13
D)20
E)23
Rationale: We want to minimize not maximize the expression,.
R=x/20+(410-x)*3/10=123+x/20-3x/10=123-5x/20 --> maximize x to minimize the expression --> x must be the greatest multiple of 20 less than 410, so 400 --> 123-5*400/20=23.
But i'm guessing 123-5x/20 can be written as 123- x/4
if x has to be the greatest multiple of 4 less then 410, then it would be 408.
Hence 123-408/4 --> 123-102 -->21
Yes, you cannot reduce in this case. If x=408, then 5/100*x and (410-x)*3/10 won't be integers.E
Answer: E
Question: In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent X of his family’s total income?
Options:
A) 15%
B) 17%
C) 24%
D) 30%
E) 33%
Rationale: Lets suppose the Total Family income in Feb = 100x
Wilson's earning in Feb = 40% of 100x = 40x
Earnings of remaining family in Feb = 100x - 40x = 60x
Wilson's earning in March = 75% of Wilson's Feb earnings = 75% of 40x = 30x
Earnings of remaining family in March = Earnings of remaining family in Feb = 60x
Thus Wilson's earning as % of Total family income in March X= 30x/ (30+60)x = 30x/90x = 33.33%
Thus Answer is E
Answer: E
Question: If a > 1, which of the following is equal to (2a + 4)/(a^2 + 2a - 3)?
Options:
A)2(a+2)/(a+3)(a-1)
B)a + 3
C)2/(a - 1)
D)2a/(a - 3)
E)(a - 1)/2
Rationale: Here's the algebraic approach:
(2A + 4)/(A^2 + 2A - 3) can be rewritten as...
2(A + 2)/(A+3)(A-1)
We can simplify the fraction, which leaves us with...
Ans : A
Answer: A
Question: If you write down all the numbers from 1 to 100, then how many multiples of 3 ?
Options:
A)A)32
B)B)38
C)C)30
D)D)31
E)E)33
Rationale: Division rule for 3 - sum of all digits is multiple of 3
3 6 9 12 15 18 21 24 27 30
33 36 39 42 45 48 51 54 57 60
63 66 69 72 75 78 81 84 87 90
93 96 99
Ans - E
Answer: E
Question: What is the CP of Rs 100 stock at 7 discount, with 1/5% brokerage?
Options:
A)93.2
B)96.2
C)97.5
D)98.25
E)None of these
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-7+1/5
93.2
Thus the CP is Rs 93.2.
ANSWER A
Answer: A
Question: If a fair die is rolled five times, what is the probability that a 3 occurs on at least one roll?
Options:
A)25/36
B)125/216
C)64/107
D)11/36
E)36/216
Rationale: Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1-(5/6)(5/6)(5/6)(5/6)(5/6) = 1-43/107 = 64/107.
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
C is thus the correct answer.
Hope this helps.
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)160 m
B)190 m
C)120 m
D)180 m
E)150 m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer: D
Answer: D
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
Options:
A)10590
B)10500
C)10129
D)11129
E)10510
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3 : 4.
Simran's share = Rs. ( 24500 * 3/7)
= Rs. 10500.
Answer: B
Answer: B
Question: 3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 2 men and 2 women will do that task.
Options:
A)3/7
B)3/10
C)3/18
D)3/16
E)3/11
Rationale: 3 m + 8 w = 6 m + 2 w
3 m = 6 w
1 m = 2 w
Therefore 3 m + 8 w = 14 w
2 m + 2 w =6 w
Answer is 6/14 =3/7
Answer: A
Answer: A
Question: What is the probability for a family with three children to have a girl and two boys (assuming the probability of having a boy or a girl is equal)?
Options:
A)1/8
B)1/4
C)1/2
D)3/8
E)5/8
Rationale: One possible case is: girl - boy - boy
The probability of this is 1/2*1/2*1/2= 1/8
There are 3C2 = 3 such cases so we should multiply by 3.
P(one girl and two boys) = 3/8
The answer is D.
Answer: D
Question: Which of the following fractions is greater than 1/2 and less than 9/10?
1. 1/2 2. 9/10 3. 1/3 4. 1/9 5. 3/4 6. 1/10
Options:
A)1/2
B)3/5
C)1/10
D)1/3
E)9/10
Rationale: 1/2= 0.5, 9/10 = 0.9, 1/3= 0.33, 1/9= 0.11, 3/5= 0.6, 1/10= 0.1
Clearly, 0.6 lies between 0.50 and 0.9.
Therefore, 3/5 lies between 1/2 and 9/10
Answer is B.
Answer: B
Question: The difference between the squares of two consecutive odd integers
is a square<1000 whose root equals the combined sum of the digits
of the two integers. What is the sum of the digits of the larger integer?
Options:
A)2
B)5
C)8
D)10
E)11
Rationale: Assume two odd integers to be (2x-1) and (2x+1).
Difference of their squares = (2 x+1)^2 - (2x-1)^2
= 4x^2 + 1 + 4x - (4x^2 + 1 - 4x)
= 4x^2 + 1 + 4x - 4x^2 - 1 + 4x
= 8x
Now root of 8x needs to be an integer such that it is equal to the sum of the digits of the two odd integers.
8 = 2^3, so x needs to be such that it "completes" a perfect square.
If we find x, we can find the value of 2x+1 (larger integer) and then sum of its digits.
Let's check the options, starting with c.
For sum to be 8, few possibilities are: 17, 35, 53, 71
If we take 17, the pair is 15 and 17, meaning x = 8.
8x = 64
root of 64 = 4 but 4 is not equal to 1+5+1+7.
Reject.
If we take 35, the pair is 33 and 35, meaning x = 17.
8x = 8*17
Reject since perfect square is not possible.
If we take 53, the pair is 51 and 53, meaning x = 26.
8x = 8*26
Reject since perfect square is not possible.
If we take 71, the pair is 69 and 71, meaning x = 35.
8x = 8*35
Reject since perfect square is not possible.
I tried each option and the possibilities and then got lost.
Then, it occurred to me that I was only checking 2-digit integers. What about 3-digits?
Starting with option a, only 2-digit odd integer whose sum is 2 is 101.
If we take 101, the pair is 99 and 101, meaning x = 50.
8x = 8*50 = 400
root of 400 = 20 which is indeed equal to 9+9+1+1.
Answer (A).
Answer: A
Question: P , Q and R started a business by investing Rs 120000 , Rs 135000 & Rs 150000 respectively. Find the share of each, out of the annual profit of Rs 56700
Options:
A)16800 , 18900 , 21000
B)17850 , 18900 , 21000
C)16800 , 18900 , 22000
D)17850, 18500 , 22000
E)None of these
Rationale: Explanation :
P : Q : R = 120000 : 135000 : 150000 = 120:135:150
= 24:27:30
= 8:9:10
Share of P= 56700*8/27 = 2100*8 = 16800
Share of Q = 56700*9/27 = 2100*9 = 18900
Share of R = 56700*10/27 = 2100*10 = 21000. Answer : Option A
Answer: A
Question: The arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
Options:
A)10.5
B)11
C)11.5
D)12
E)12.5
Rationale: The value which isexactlytwo SD less than the mean is:mean-2*SD=15.5-2*1.5=12.5.
Answer: E.
Answer: E
Question: A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the three fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
Options:
A)240
B)720
C)144
D)336
E)420
Rationale: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,
5!*3! =120*6=720
Answer is B
Answer: B
Question: A student multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation ?
Options:
A)22
B)64
C)365
D)29
E)36
Rationale: Let the number be x.
Then, ideally he should have multiplied by x by 5/3. Hence Correct result was .
By mistake he multiplied x by 3/5 . Hence the result with error =
Then, error =
Error % = = 64 %
Answer: B
Answer: B