Greatest Number

[karthikpandian19]

Which of the following numbers is the greatest?
A.
1876455/1876452
B.
1883449/1883446
C.
1883456/1883453
D.
1883459/1883456
E.
1883494/1883491

[Anurag@Gurome]

Deleted

[user123321]

modified:should be A

say for example, we know that 4/3 is greater than 5/4 & 5/4 is greater than 6/5...
so likewise,if numerator and denominator for a set of numbers has same difference, the number with less numerator or denominator is the largest among them.

user123321

[sk8legend408]

Since the difference between each of the answer choice's numerators and denominators is three, you have to choose the lowest of the numbers because that will yield the greatest answer. The higher number you divide by with the same difference, 3, the lower the answer will be.

All answer choices except A are over 1,880,000 so the answer is A since it is the smallest number.

You can even check with a calculator to confirm.

[user123321]

Since the difference between each of the answer choice's numerators and denominators is three, you have to choose the lowest of the numbers because that will yield the greatest answer. The higher number you divide by with the same difference, 3, the lower the answer will be.

All answer choices except A are over 1,880,000 so the answer is A since it is the smallest number.

You can even check with a calculator to confirm.

silliest mistake i did. thanks.

user123321

[GMATGuruNY]

Which of the following numbers is the greatest?
A.
1876455/1876452
B.
1883449/1883446
C.
1883456/1883453
D.
1883459/1883456
E.
1883494/1883491

Scanning the answer choices A-B-C-D-E, note the following:
Both the numerator and the denominator keep increasing.
In each case, numerator - denominator = 3.

Plug in easier numbers that follow the same pattern:

A: 4/1 = 4
B: 5/2 = 2.5
C: 6/3 = 2
D: 7/4 = 1.75
E: 8/5 = 1.6

The greatest value is A.

When you don't know what number property rule is being tested:

1. PLUG IN EASIER NUMBERS.
2. LOOK FOR A PATTERN.

[karthikpandian19]

The question is correct

OA is A

Which of the following numbers is the greatest?
A.
1876455/1876452
B.
1883449/1883446
C.
1883456/1883453
D.
1883459/1883456
E.
1883494/1883491

Can you check the question once again? It doesn't seem to be correct.

[Anurag@Gurome]

The question is correct

OA is A

Got it Karthik, the question is correct. Thanks.

[Rastis]

GMATGuruNY,

How did you choose the numbers that you plugged in? I do not understand.

[pemdas]

my dear friend, this question as well as many others which will be tested on GMAT do not need solution as long as you know two simple rules which proceed from the theory of large numbers; I incidentally derived the rules for myself recently

Rule 1: whenever you compare large numbers in a numerator and a denominator, if the numerator is less than the denominator this number will be tending to the value of 1/2. The larger the numbers in the numerator and the denominator the closer the number to the value of 1/2.

Rule 2: whenever you compare large numbers in a numerator and a denominator, if the numerator is greater than the denominator this number will be extended from the value of 1/2. The less the numbers in the numerator and the denominator the farther the number from the value of 1/2.

Now look at your answer choices and decide in one single click (like 10-15 second of screening numbers) and mark the correct A.

I also agree simplifying and picking good numbers is good strategy for GMAT, as Mitch explains, but here there's more convenient method rooted in the theory of large numbers.

[spoiler]You could google this theory as well, but it's very complicated and has implications of probability theory.[/spoiler]

Which of the following numbers is the greatest?
A.
1876455/1876452
B.
1883449/1883446
C.
1883456/1883453
D.
1883459/1883456
E.
1883494/1883491

[Rastis]

pemdas,

Your explanation went way over my head. Is there a different way of explaining it? I'm probably more confused now than I was before.

[GMATGuruNY]

GMATGuruNY,

How did you choose the numbers that you plugged in? I do not understand.

The problem offers messy numbers to test a basic number property rule.
To determine what rule is being tested, I plugged in easier numbers that follow the same pattern as the messy numbers given in the problem.
The basic question is this:

If a,b,c,d and e are positive integers such that a<b<c<d<e, which of the following is greatest?

A. (a+3)/a
B. (b+3)/b
C. (c+3)/c
D. (d+3)/d
E. (e+3)/e

Plugging in a=1, b=2, c=3, d=4, d=5 results in the following:
A: 4/1 = 4
B: 5/2 = 2.5
C: 6/3 = 2
D: 7/4 = 1.75
E: 8/5 = 1.6

The greatest answer choice is A.

The easier numbers show the rule that is being tested:
If x<y<0 and c>0, then:
(x+c)/x > (y+c)/y

An alternate approach to the problem above would be to rewrite all of the answer choices in the form (x+c)/x:
A. 1876455/1876452
(1876452 + 3)/1876452
1 + 3/1876452

B. 1883449/1883446
(1883446 + 3)/1883446
1 + 3/1883446

C. 1883456/1883453
(1883453 + 3)/1883453
1 + 3/1883453

D. 1883459/1883456
(1883456 + 3)/1883456
1 + 3/1883456

E. 1883494/1883491
(1883491 + 3)/1883491
1 + 3/1883491

Comparing the answer choices:
The only difference is the fraction being added to 1.
Since the denominator increases as we proceed from A to E -- while the numerator stays the same -- the resulting fractions keep getting smaller.
Thus, the greatest answer choice is A.

Here are two other problems in which I plugged in easier numbers in order to determine the number property rule being tested:

https://www.beatthegmat.com/og-12-proble ... 00085.html

https://www.beatthegmat.com/matdfhfg-t83392.html

[Rastis]

I'm sorry but I just cannot grasp the logic in this. I think this will be one of those problems that I'll just guess on...if I even get to that level of question. Thanks though.

[GMATGuruNY]

I'm sorry but I just cannot grasp the logic in this. I think this will be one of those problems that I'll just guess on...if I even get to that level of question. Thanks though.

Let's focus on the last approach that I offered.

If we divide 3 by ever increasing numbers, the resulting quotients keep getting smaller:
3/1 = 3
3/2 = 1.5
3/100 = .03
In other words, if the numerator stays the same, but the denominator INCREASES, the resulting fraction gets SMALLER.

Onto answer choices A and B.
In each case:
Numerator = denominator + 3.
Bearing this is mind, let's substitute (denominator +3) for each numerator, then simplify:

A. 1876455/1876452
(1876452 + 3)/1876452
1876452/1876452 + 3/1876452
1 + 3/1876452

B. 1883449/1883446
(1883446 + 3)/1883446
1883446/1883446 + 3/1883446
1 + 3/1883446

Just as 3/2 > 3/100 , so too 3/1876452 > 3/1883446.
In each case, the numerator stays the same, while the denominator INCREASES.
The result is a SMALLER fraction.
Thus, A > B.

Does this help?

[Rastis]

Not really. The numbers that you have put together are just confusing me even more. I think even if I could understand how you you derived the answer, I could never have thought to use that type of logic.