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Directions (1-15): Find the wrong term which does not follow the pattern that other numbers follow
in the following number series:
Q1. 28, 66, 128, 224, 348, 518
(a) 348
(b) 224
(c) 66
(d) 518
(e) 28
Q2. 12, 22, 63, 246, 1235, 7404
(a) 246
(b) 7404
(c) 12
(d) 63
(e) 1235
Q3. 1634, 905, 562, 439, 410, 409
(a) 439
(b) 410
(c) 409
(d) 1634
(e) 905
Q4. 5, 25, 129, 780, 5441, 43529
(a) 5441
(b) 129
(c) 25
(d) 780
(e) 5
Q5. 16, 40, 100, 250, 630, 1562.5
(a) 630
(b) 40
(c) 16
(d) 100
(e) 250
Directions (11-15): In the given question, two equations numbered I and II are given. You have to solve both the equations andGive answer:
(a) If x < y
(b) If x > y
(c) If x ≥ y
(d) If x ≤ y
(e) If relationship between x and y cannot be established.
Q11. I. 2x² - 7x+ 3 = 0
II. 2y² - 7y + 6 = 0
Q12. I. 4x² + 16x +15 = 0
II. 2y² + 3y + 1 = 0
Q13. I. 9x² - 45x + 56 = 0
II. 4y² - 17y + 18 = 0
Q14. I. 2x² + 11x + 14 = 0
II. 2y² + 15y + 28 = 0
Q15. I. 6x² + 11x + 4 = 0
II. 4y² - 7y – 2 = 0
SOLUTION
S1. Ans.(b)
Sol. Pattern is
3³ + 1 = 28
4³ + 2 = 66
5³+ 3 = 128
6³ + 4 = 220
7³ + 5 = 348
8³ + 6= 518
∴ Wrong term = 224
S2. Ans.(a)
Sol.
Wrong number = 246
S3. Ans.(a)
Sol. Pattern is
–9³, –7³, –5³, –3³, –1³
∴ Wrong term = 439
S4. Ans.(d)
Sol. Pattern is
×4 + 5, ×5+ 4, × 6 + 3, × 7+2, ×8 +1
∴ Wrong term = 780
S5. Ans.(a)
Sol. Pattern is
16 × 2.5 = 40
40 × 2.5 = 100
100 × 2.5 = 250
250 × 2.5 = 625
625 × 2.5 = 1562.5
So, 630 is wrong term
S11. Ans.(e)
Sol.
I. 2x² - 7x+ 3 =0
⇒ 2x² - 6x – x + 3 = 0
⇒ (x- 3) (2x- 1) = 0
x =3, 1/2
II. 2𝑦
2 − 7𝑦 + 6 = 0
⇒ 2y² - 4y -3y+ 6 = 0
⇒ (y- 2) (2y - 3) = 0
⇒ 𝑦 = 2,
3/2
No relation between x & y
S12. Ans.(a)
Sol.
I. 4𝑥
2 + 16𝑥 + 15 = 0
⇒ 4𝑥
2 + 10𝑥 + 6𝑥 + 15 = 0
⇒ (2x + 5) (2x + 3) = 0
⇒ 𝑥 =
,-5/2
−3/2
II. 2𝑦
2 + 3𝑦 + 1 = 0
⇒ (2y+ 1) (y+ 1) = 0
⇒ 𝑦 = −1, −1/2
y>x
S13. Ans.(b)
Sol.
I. 9x² - 45x + 56 = 0
⇒ 9x² - 21x – 24x + 56 = 0
⇒ (3x – 7) (3x- 8) = 0
⇒ 𝑥 =7/3,8/3
II. 4𝑦
2 − 17𝑦 + 18 = 0
⇒ 4y² - 8y – 9y + 18 = 0
⇒ (y- 2) (4y- 9) = 0
⇒ y= 2, 9/4
x >y
S14. Ans.(c)
Sol.
I. 2x² + 11x + 14 = 0
⇒ 2x² + 4x+ 7x+ 14 = 0
⇒ (x+ 2) (2x+ 7) = 0
⇒ x = -2, -7/2
II. 2y² + 15y + 28 = 0
⇒ 2y² + 8y+ 7y+ 28 = 0
⇒ (y+ 4) (2y+ 7) = 0
⇒ y = -4, −7/2
x ≥ y
S15. Ans.(a)
Sol.
I. 6x² + 11x+ 4 = 0
⇒ 6x² +8x+ 3x+ 4 = 0
⇒ (3x+ 4) (2x+ 1) = 0
⇒ x = −4/3
, −1/2
II. 4𝑦
2 − 7𝑦 − 2 = 0
⇒ 4y² - 8y +y – 2 = 0
⇒ (y – 2) (4y+ 1) = 0
⇒ 𝑦 = 2, −1/4
y > x
