Which of the following is least?

Question

Which of the following is least? A. -32/73 B. -13/23 C. -12/25 D. -8/17 E. -7/16 2024-01-27_15-16-04.png

Bunuel · Accepted Answer

Observe that all the fractions, except B, -13/23, have absolute values less than 1/2 (since their numerators are smaller than half of their denominators). This makes them greater than -1/2 when negative. In contrast, -13/23 has an absolute value greater than 1/2, making it less than -1/2. Therefore, the least among these options is B.

Answer: B.

chetan2u · Answer

Easiest way would be

All negative numbers, so the highest absolute value will be the lowest. 
A very simple observation will get you the answer.

The denominators in all the options are more than two times the numerator except one fraction.  
A.  |-\frac{32}{73}|=\frac{32}{2*32+9}

B. -13/23 |-\frac{13}{23}|=\frac{13}{2*13-3}

C. -12/25 |-\frac{12}{25}|=\frac{12}{2*12+1}

D. -8/17 |-\frac{8}{17}|=\frac{8}{2*8+1}

E. -7/16 |-\frac{7}{16}|=\frac{7}{2*7+2}

Thus,  \frac{13}{23}  is the largest and becomes the smallest when ‘-‘ sign is placed in front.

B

gmatophobia · Answer

We can the concept of approximation to determine the approximate value of each fraction and then compare the options to determine the least

A. -32/73

-\frac{32}{64} = -0.5

As the denominator, 73, is greater than 63, the value,  -\frac{32}{73} , is greater than -0.5

B. -13/23

-\frac{13}{26} = -0.5

As the denominator, 23, is less than 26, the value,  -\frac{13}{26} , is less than -0.5

C. -12/25

-\frac{12}{24} = -0.5

As the denominator, 25, is greater than 24, the value,  -\frac{12}{24} , is greater than -0.5

D. -8/17

-\frac{8}{16} = -0.5

As the denominator, 17, is greater than 16, the value,  -\frac{8}{16} , is greater than -0.5

E. -7/16

-\frac{7}{14} = -0.5

As the denominator, 16, is greater than 14, the value,  -\frac{7}{14} , is greater than -0.5

Hence, only the value of the fraction in Option B is less than  -0.5 . Hence,   Option B   has the least value.

pappal · Answer

whichever absolute value is largest the -ve value will be least. taking absolute values:
32/73, 13/23, 12/25, 8/17, 7/16
13/23>12/25 so discard the latter
13/23=39/69 > 32/73 so discard the latter
now 8*16/17*16=128/17*16 > 7*17/17*16=119/17*16 (making denominators same) so discard the latter
finally 13*17/23*17 > 8*23/17*23, so discard the latter
hence largest absolute value is 13/23 so  -13/23 is the least. B 
 *thanks Banuel for suggesting a less than 15 secs approach*

Which of the following is least?

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Which of the following is least?

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