If 3a=4b=6c and a+b+c=2729 , then a2+b2+c2 =? 81 83 87 None of these 4 b = 6 c ?

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Home ‣ Aptitude ‣ Square Root and Cube Root Comments

Question
If 3a=4b=6c and a+b+c=2729 , then a2+b2+c2 =?
Options
A. 81
B. 83
C. 87
D. None of these

Correct Answer

87

Explanation

$4 b = 6 c ? b = \frac{3}{2} c a n d 3 a = 4 b ? a = \frac{4}{3} b = \frac{4}{3} (\frac{3}{2} c) = 2 c$

$a + b + c = 27 \sqrt{29} ? 2 c + \frac{3}{2} c + c = 27 \sqrt{29} ? c = 6 \sqrt{29}$

$? \sqrt{a^{2} + b^{2} + c^{2}} = \sqrt{(a + b + b)^{2} - 2 (a b + b c + c a)}$

$= \sqrt{(27 \sqrt{29})^{2} - 2 (2 c � \frac{3}{2} c + \frac{3}{2} c � c + c � 2 c)}$

$= \sqrt{(729 � 29) - 2 � \frac{13}{2} c^{2}}$

= 87

Square Root and Cube Root problems

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1. The value of 80-11245-63 is:
Options
A. 3/4
B. 4/3
C. 4/7
D. 7/4

Discuss

Correct Answer: 4/3

Explanation:

$\frac{\sqrt{80} - \sqrt{112}}{\sqrt{45} - \sqrt{63}} = \frac{\sqrt{16 � 5} - \sqrt{16 � 7}}{\sqrt{9 � 5} - \sqrt{9 � 7}} = \frac{4 \sqrt{5} - 4 \sqrt{7}}{3 \sqrt{5} - 3 \sqrt{7}}$

$= \frac{4 (\sqrt{5} - \sqrt{7})}{3 (\sqrt{5} - \sqrt{7})} = \frac{4}{3}$

2. 0.01+0.0064 =?
Options
A. 0.03
B. 0.3
C. 0.42
D. None of these

Discuss

Correct Answer: 0.3

Explanation:

$\sqrt{0.01 + \sqrt{0.0064}} = \sqrt{0.01 + \sqrt{\frac{64}{10000}}} = \sqrt{0.01 + \frac{8}{100}} = \sqrt{0.01 + 0.08} = 0.3$

3. If 35+125=17.88 , then what will be the value of 80+65 =?
Options
A. 13.41
B. 20.46
C. 21.66
D. 22.35

Discuss

Correct Answer: 22.35

Explanation:

$3 \sqrt{5} + \sqrt{125} = 17.88 ? 3 \sqrt{5} + 5 \sqrt{5} = 17.88$

$? \sqrt{5} = 2.235$

$? \sqrt{80} + 6 \sqrt{5} = 4 \sqrt{5} + 6 \sqrt{5} = 10 \sqrt{5} = 10 � 2.235 = 22.35$

4. 1.52 x 0.0225 = ?
Options
A. 0.0375
B. 0.3375
C. 3.275
D. 32.75

Discuss

Correct Answer: 0.3375

5. If 5+237+43 = a + b3 then a & b = ?
Options
A. a=-11,b=-6
B. a=-11,b=6
C. a=11,b=-6
D. a=11,b=6

Discuss

Correct Answer: a=11,b=-6

6. If x = 2 + 223 + 213 then find the value of x3-6x2+6x ?
Options
A. 1
B. 2
C. 3
D. 4

Discuss

Correct Answer: 2

Explanation:

Given that $x = 2 + 2^{\frac{2}{3}} + 2^{\frac{1}{3}}$

So x - 2 = $2^{\frac{2}{3}} + 2^{\frac{1}{3}}$

Now cubing on both sides, we get

=> $x^{3} - 8 - 6 x^{2} + 12 x = 4 + 2 + 6 (x - 2)$

Therefore, $x^{3} - 6 x^{2} + 6 x = - 6 + 8 = 2$

7. 28?+1426=34 of 2872
Options
A. 576
B. 676
C. 1296
D. 1444

Discuss

Correct Answer: 676

Explanation:

$L e t 28 \sqrt{x} + 1426 = 3 � 718$

Then $28 \sqrt{x} = 2154 - 1426$

$? 28 \sqrt{x} = 728 ? \sqrt{x} = 26$

$? x = 676$

8. Find the value of 1.21x0.91.1x0.11 ?
Options
A. 0
B. 1
C. 3
D. 5

Discuss

Correct Answer: 3

Explanation:

Given $\sqrt{\frac{1.21 x 0.9}{1.1 x 0.11}}$

= $\sqrt{\frac{1.21 x 100 x 0.9 x 10}{1.1 x 10 x 0.11 x 100}}$

= $\sqrt{9}$

= 3.

9. If x�y = x + y + xy , the value of 6x24 is:
Options
A. 41
B. 42
C. 43
D. 44

Discuss

Correct Answer: 42

Explanation:

$G i v e n x � y = x + y + \sqrt{x y} H e r e x = 6, y = 24 T h e n, x � y = 6 + 24 + \sqrt{6 x 24} 6 x 24 = 30 + \sqrt{144} = 30 + 12 = 42 .$

10. What should come in place of x in the following equation? x 128 = 162 x
Options
A. 13
B. 12
C. 17
D. 16

Discuss

Correct Answer: 12

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If 3a=4b=6c and a+b+c=2729 , then a2+b2+c2 =?

Square Root and Cube Root problems

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