NTA NET paper 1 December 2018 Mathematical Reasoning

18th Morning Dec 2018 Session

1. If NTA14 and NTA15 are 5-digit numbers such that their sum is 157229, then N+T+A would be:
   1. Options:-
      1. 25
      2. 72
      3. 21
      4. 15
         1. NTA+NTA = 157229
         2. 2(NTA) = 1572
         3. NTA =786
         4. N=7T=8A=6
         5. N+T+A = 7+8+6 = 21
2. In the sequence of numbers 5, 19, 49, 101, 181, 295, x,……, the term x is:
   1. Options:-
      1. 501
      2. 449
      3. 351
      4. 401
      5. Solution:
         1. 5, 19, 49, 101, 181, 295
         2. 1st gap – 14, 30, 52, 80,114
         3. 2nd gap – 16, 22, 28, 34
         4. 3rd gaps – 6,6,6 so adding last terms from each sequence – 295+114+34+6 = 449
3. You have recently joined a new office. Walking at 5 km/hour, you reach the office from your house 15 minutes early and walking at 3 km/hour, you are late by 9 minutes. The distance between your house and office is : Options:-
   1. 1. 5 km
      2. 3 km
      3. 2 km
      4. 8 km
      6. Solution:
         1. Let t be the time taken to reach the office from home.
         1. 5/60* t(t-15) = 3/60 (t+9)
         1. 5t-75 = 3t+27 so t=51
         2. D = 5/60*(51-15) = 1/12*36 = 3 km
4. Choose the correct alternative to replace the question mark (?).
   1. 42—> 26
   2. 71—>78
   3. 33—>16
   4. 62—>?
   1. ^Options:-
      1. 54
      2. 68
      3. 38
      4. 39
      5. Solution:
      6. 4+2 = 6, 4/2 = 2 so 42 –> 26 similarly for 62 — > 38

18th Afternoon Dec 2018 Session:

1. ^{Rs.9000 were divided among a certain number of persons. Had there been 20 more} persons, each would have got Rs.160 less. The original number of persons was:
   1. Options:
      1.55  _{2.25  3.30  4. 45}
      1. _Solution:
      2. _{Let x be the number of persons,}
      3. _{Assuming that. rs 9000 has been divided equally among the persons each person got = 9000/x+20}
      5. _{9000/x-9000/x+20 = 160}
      6. _{9000(x+20) – 9000x/x(x+20) = 160}
      7. _{9000x + 180000-9000x/x(x+20) = 160}
      8. _{180000/x(x+20) = 160}
      9. _{1125 = x(x+20)}
      10. _{x^2+20x-1125 = 0}
      11. _{x^2 + 45x-25x-1125 = 0}
      12. _{x(x+45) -25(x+45) = 0}
      13. _{(x+45)(x-25) = 0}
      14. _{x= -45 or x =25}
          1. Originally there were 25 persons who receives rs.360 but later increased to 45 persons, 9000/45 = 200, so 360-200 = 160 less.
2. The number of marble slabs of size 20 cm × 30 cm required to pave the floor of a square room of side 3 meters is:
   1. Options:
      1. 225
      2. ₁₀₀
      3. ₂₅
      4. ₁₅₀
   1. _Solution:
   2. 1 m = 100 cm,
   3. _{Since the side is 3m = 300cm, area = 90000} cm^2
   4. Area of 1 slab = 20*30 = 600 cm^2
   5. _{No. of marble slabs = 90000/600 = 150}
3. In the sequence of number 2,8,26,62,122,212,X,….the term x is: Reference:
   1. Options:
      1. 248
      2. 302
      3. 338
      4. 332
      5. Solution:
         1. 2+6 = 8 + 18 = 26+36 = 62+60 = 122+90 = 212
         1. Difference between the numbers in the series- 6,18,36,60,90,126
         2. Further Difference, +12,+18, +24,+30+36
         3. So, X=212+126=338.

19th Morning Dec 2018 Session:

1. In the sequence of numbers 2, 8, 24, 64, 160, x,……….., the term x is:
   1. 320
   2. 384
   3. 224
   4. 192
   5. Solution:
      1. 2^1*1 = 2
      2. 2 ^ 2 * 2 = 8
      3. 2 ^3 * 3 = 24
      4. 2 ^4 * 4 = 64
      5. 2^5*5 =160
      6. 2^6 *6 = 384
2. A man traveled 300 km by train and 200 km by taxi, and he completed this journey in 5 hours and 30 minutes. However, if he travels 260 km by train and 240 km by taxi, it will take 6 minutes more to complete the journey. The speed of the train is:
   1. 80 km/hour
   2. 100 km/hour
   3. 120 km/hour
   4. 110 km/hour
      1. Solution: Let x be the speed of train and y be the speed of taxi.
      1. 300/x + 200/y = 5+1/2(11/2)
      1. 260/x + 240/y = 5+3/5 (5 36/60 = 28/5)
      2. On solving above 1 and 2,
      3. 600 y+400x = 11xy   * 3 = > 1800y+1200x = 33 xy
      4. 1300y + 1200x = 28 xy => 1300y+1200x = 28 xy
      5. Speed of trian(x) = 100 km/hr and
         1. Speed of taxi (y) = 80 km/hr.
3. The present age of the father to that of the elder son. Ten years hence the age of the father will be three times that of the younger son. If the difference in ages of the two sons is as 15 years, the present age of the father is:
   1. Options:-
      1. 70 years
      2. 110 years
      3. 50 years
      4. 60 years
         1. Solution:–
         2. Let “x” be the present age of the elder son.
         3. Age of older son = (x+15)
         4. Father’s age = 2(x+15)
         5. By question 10 years hence,
            1. 2(x+15)+10 = 3(x+10)
            2. 2x+30+10 = 3x+30,
            3. 40-30 = x = 10 yrs
            4. Father’s age = 2(10+15) = 50 years
         6. Reference:

19th Afternoon Dec 2018 Session

1. The next term in the series 7, 11, 19, 35, 67, _________ is.
   1. 131
   2. 133
   3. 99
   4. 121
   5. Solution:
      1. 7,11,19,35,67,131
      2. +4,+8,+16,+32,+64 , 67+64 = 131

20th Morning Dec 2018 Session

1. The next number in the series 12, 15, 21, 33, 57, _______ is:
   1. Options:-
      1. 105
      2. 97
      3. 95
      4. 107
         1. Solution:
            1. 12+3=15
            2. 15+6=21
            3. 21+12=33
            4. 33+24=57
            5. 57+48=105

20th Afternoon Dec 2018 Session

1. The next term in the series is: 56, 40, 27, 17, 10, _________
   1. Options:-
      1. 7
      2. 8
      3. 6
      4. 5
         1. Solution:
         2. Difference – 16, 13, 10, 7, 4
         3. Common difference – 3
         4. X = 6
         5. 56 – 40 = 16
         6. 40- 27 = 13
         7. 27- 17 = 10
         8. 17-10 = 7
         9. 10 -? = 4

21st December 2018 First Shift:

1. The next term in the number series 10, 13, 22, 49, _______.
   1. Options:-
      1. 89
      2. 97
      3. 130
      4. 126
         1. Solution:
         2. Difference – 3,9,27,81
         3. Multiplicant – 3*3 = 9, 9*3 = 27, 27*3 = 81
         4. So, 81+49 = 130

21st December 2018 Second Shift:

1. the next term in the number series 41, 27, 16, 8, ______ is:
   1. Options:-
      1. 2
      2. 3
      3. 4
      4. 1
      1. Solution: 41-14 = 27, 27-11 = 16, 16-8 = 8, 8-5 = 3
      2. 5,8,11,14 with 3 gap difference
2. 9000 were divided among a certain number of persons. Had there been 20 more persons each would have got rs.160 less. The original number of persons was
   1. Solution:
      1. 9000/x  – 9000/x+20 = 160
      2. 9000x + 180000 – 9000x/ x(x+20) = 160,
      3. 1125 = x(x+20)
      4. Solving for x = 25
3. Number of marble slabs of size 20 cm * 30 cm required to pave the floor of a square room of side 8 mts
   1. Solution:
      1. 3*3 = 9 m^2
      2. so 1 m^2 = 10000 cm^2
      3. 20 *30 = 600 cm^2  so 9*10000/600 = 150

22 December 2018 First Shift:

1. The next term in the series 0, 1, 9, 36, 100, __________ is:
   1. Options:-
   1. 225
   1. 196
   1. 216
   2. 164
   3. Solution:
      1. 1^2 = 1,
      2. 3^2 = 9,
      3. 6^2 = 36
      4. 10^2 = 100
      5. 15^2 = 225
         1. terms indicates 0^2,1^2, 3^2, 6^2, 10^2,
         2. difference between the squares are 1,2,3,4,5 so next term is 15^2.

22 December 2018 Second Shift

1. Before death, a man left the following instructions for his fortune: half to his wife; 1/7 of what was left to his son; 2/3 of what was left to his daughter; the man’s pet dog got the remaining ^{Rs. 20000. How much money did the man leave behind altogether?}
   1. Rs. 100000 2. Rs. 70000 3. Rs. 140000 4. Rs. 40000
   2. Solution:
   3. Let the total amount be x
   4. He gave half of this amount to his wife
   5. So, wife’s share = (1/2)x
   6. Remaining amount = x/2
   7. 1/7 of what was left to his son
   8. son’s share = 1/7 of x/2
   9. Remaining amount = x/2 – x/14 = 3x/7
   10. 2/3 of what was left to his daughters = 2/3 of ((1/7) pf (1/2)x)
   11. Daughter’s share = 2/3(3x/7) = 2x/7
   12. Remaining amount = 3x/7 – 2x/7 = x/7
   13. man’s dog got the remaining rs.20000 =x/7
   14. x = 140000 Hence the man leave Rs.140000 behind altogether
2. if  R+1/s=1, and S+1/t=1, then R*S*T and , then =_____________.
   1. Options:-
      1. -2
      2. 2
      3. -1
      4. 1
3. in the sequence of numbers 1, 2, 6, 33, 49, 174, 210, x,……., the term x is:
   1. Options:-
   2. 553
   3. 444
   4. 510
   5. 259
      1. Solution:
      2. 2-1=1 which is cube of 1.
      3. 6-2=4 which is square of 2.
      4. 33-6=27 which is cube of 3.
      5. 49-33=16 which is square of 4.
      6. 174-49 = 125 cube of 5
      7. 210-174 = 36 square of 6
      8. x-210 = 343
      9. So, x = 553
      10. cube of 7 which is 343
      11. Reference: