Aptitude

Question: 217 x 217 + 183 x 183 = ?

[A].

79698

[B].

80578

[C].

80698

[D].

81268

Answer: Option B

Explanation:

(217)2 + (183)2	= (200 + 17)2 + (200 – 17)2
	= 2 x [(200)2 + (17)2]       [Ref: (a + b)2 + (a – b)2 = 2(a2 + b2)]
	= 2[40000 + 289]
	= 2 x 40289
	= 80578.

Question: 107 x 107 + 93 x 93 = ?

[A].

19578

[B].

19418

[C].

20098

[D].

21908

Answer: Option C

Explanation:

107 x 107 + 93 x 93	= (107)2 + (93)2
	= (100 + 7)2 + (100 – 7)2
	= 2 x [(100)2 + 72]       [Ref: (a + b)2 + (a – b)2 = 2(a2 + b2)]
	= 20098

Question:
1397 x 1397 = ?

[A].

1951609

[B].

1981709

[C].

18362619

[D].

2031719

Answer: Option A

Explanation:

1397 x 1397	= (1397)2
	= (1400 – 3)2
	= (1400)2 + (3)2 – (2 x 1400 x 3)
	= 1960000 + 9 – 8400
	= 1960009 – 8400
	= 1951609.

Question:
1904 x 1904 = ?

[A].

3654316

[B].

3632646

[C].

3625216

[D].

3623436

Answer: Option C

Explanation:

1904 x 1904	= (1904)2
	= (1900 + 4)2
	= (1900)2 + (4)2 + (2 x 1900 x 4)
	= 3610000 + 16 + 15200.
	= 3625216.

Question:
2056 x 987 = ?

[A].

1936372

[B].

2029272

[C].

1896172

[D].

1926172

Answer: Option B

Explanation:

2056 x 987	= 2056 x (1000 – 13)
	= 2056 x 1000 – 2056 x 13
	= 2056000 – 26728
	= 2029272.

Question: 72519 x 9999 = ?
[A].

725117481

[B].

674217481

[C].

685126481

[D].

696217481

Answer: Option A

Explanation:

72519 x 9999	= 72519 x (10000 – 1)
	= 72519 x 10000 – 72519 x 1
	= 725190000 – 72519
	= 725117481.

Question:
3897 x 999 = ?

[A].

3883203

[B].

3893103

[C].

3639403

[D].

3791203

Answer: Option B

Explanation:

3897 x 999	= 3897 x (1000 – 1)
	= 3897 x 1000 – 3897 x 1
	= 3897000 – 3897
	= 3893103.

Question:
587 x 999 = ?

[A].

586413

[B].

587523

[C].

614823

[D].

615173

Answer: Option A

Explanation:

587 x 999	= 587 x (1000 – 1)
	= 587 x 1000 – 587 x 1
	= 587000 – 587
	= 586413.

Question:
The difference between the place values of two sevens in the numeral 69758472 is

[A].

0

[B].

6993

[C].

699930

[D].

None of these

Answer: Option C

Explanation:

Required difference = (700000 – 70) = 699930

Question:
5358 x 51 = ?

[A].

273258

[B].

273268

[C].

273348

[D].

273358

Answer: Option A

Explanation:

5358 x 51	= 5358 x (50 + 1)
	= 5358 x 50 + 5358 x 1
	= 267900 + 5358
	= 273258.