Rank those three in order from smallest to biggest.

Question

I. 47/150
II. 111/350
III.299/900

(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) II, III, I
(E) III, I, II

acegmat123 · Answer

I. 47/150 = 48/150 - 1/150

=0.32 - 1/150

II. 111/350 = 112/350 - 1/350

= 0.32 - 1/350

III. 299/900 = 300/900 - 1/900

= 0.33333 - 1/900

So we can say that

I < II < III

A

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DharLog · Answer

| vs ||| - 47*6/(150*6)=282/900 vs 299/900 --->||| > | | vs || - 47*7/(150*7) vs 111*3/(350*3)--->329/1050 vs 333/1050 --->|| > | and these fractions are closer than | and ||| ---> |<||<||| ----> option A

ScottTargetTestPrep · Answer

Multiplying 47/150 by 6/6, we have 47/150 x 6/6 = 282/900. So 47/150 < 299/900.

Multiplying 47/150 by 7/7 and 111/350 by 3/3, we have 47/150 x 7/7 = 329/1050 and 111/350 x 3/3 = 333/1050. So 47/150 < 111/350.

From the above, we see that 47/150 is the smallest of the three fractions. To compare 111/350 and 299/900, we will not make both to equivalent fractions of the same denominator. We will argue that, although both are less than 1/3, 299/900 is much closer to 1/3 than 111/350 is (observe that 1/3 = 300/900 and 1/3 = 111/333). So 299/900 must be the largest of the three.

Answer: A

babataer1 · Answer

You can solve this in 30 seconds:  
I. 47/150 = 50/150 - 3/150 = 1/3 - 1/50
II. 111/350 = 116.5/350 - 5/350 = (approx.) 1/3 - 1/70
III. 299 /900 = 300/900 - 1/900 = 1/3 - 1/900

1/50 > 1/70 > 1/900 
so I. most is subtracted from 1/3, then II. then III.
 Hence answer is A)

Wadree · Answer

Lets take 2 / 9 ..... One third of 9 is 3 .....and 2 is 1 less than 3 ..... So difference of the numerator ( 2 ) and one third of denominator ( 3 ) is 1 ..... Now .... Lets multiply both numerator and denominator with some numbers .....
( 2 × 2 ) / ( 9 × 2 ) = 4 / 18
( 2 × 3 ) / ( 9 × 3 ) = 6 / 27
Both 4 / 18 and 6 / 27 equals to 2 / 9 ..... But for 4 / 18 ..... Difference between numerator ( 4 ) and one third of denominator ( 6 ) is 2 ..... Which is double da difference of the numerator ( 2 ) and one third of denominator ( 3 ) in 2 / 9 .....
Again... For 6 / 27 .....difference of the numerator ( 6 ) and one third of denominator ( 9 ) is 3 ... Which is triple da difference of the numerator ( 2 ) and one third of denominator ( 3 ) in 2 / 9 .....

So now we know that multiplying both numerator and denominator of a fraction with same value will Automatically multiply da difference between numerator and one third of denominator......

Now.....lets try to make denominators of options da same.....

Lets.... ( 47 × 2 ) / ( 150 × 2 ) = 94 / 300 ..... So 94 is already 6 less than one third of 300 ......but 111 is only 5.67 less than one third of 350......so multiplying 47/ 150 anymore will only increase difference between numerator and one third of denominator......so 111 / 350 > 47 / 150

Now .... ( 111 × 2 ) / ( 350 × 2 ) = 222 / 700 ..... 222 is already 11.33 less than 233.33 which is one third of 700 ...... But 299 is only 1 less than one third of 900.... So multiplying 111 / 350 anymore will only increase difference between numerator and one third of denominator....... So 299 / 900 > 111 / 350 .....

So..... [ 47 / 150 ] < [ 111 / 350 ] < [ 299 / 900 ]

Rank those three in order from smallest to biggest.

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Rank those three in order from smallest to biggest.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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