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12 Days of Christmas GMAT Competition 2025 - Day 2: If (3.7 * 10^a)

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ikan444

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16 Dec 2025, 09:26

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(3.7*10^a)*(5.8*10^b) = 0.2146*10^c
The first thing that clicks is - what is 37*58? It's 2146 (perfect case for us)!

Let's place the elements accordingly,

(3.7*5.8)(10^a * 10^b) = 21.46*10^(c+2)
(21.46)(10^(a+b)) = (21.46)(10^(c+2))

a+b = c+2
c= a+b-2 (A)

Chaithanya20

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16 Dec 2025, 09:27

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(3.7*10^a)*(5.8*10^b)=0.2146*10^c
3.7*5.8*10^(a+b) = 0.2146*10^c
21.46*10^(a+b) = 21.46*10^(-2+c)
a+b = -2+c
c= a+b+2

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16 Dec 2025, 09:28

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(3.7 * 10^a) * (5.8* 10^b) = 0.2146* 10^c
21.46 *10^a+b = 0.2146* 10^c
0.2146*10^2 * 10^a+b = 0.2146* 10^c
0.2146 *10^a+b+2 = 0.2146^c
bases are same so equating power: c= a+b+2

prepapr

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16 Dec 2025, 09:31

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3.7 * (10^a) * 5.8 * (10^b) = 0.2146 * (10^c)
10^(a+b) = (0.2146/(3.7*5.8)) * (10^c)
= (2146/37*5800) * (10^c)
= (58/5800) * (10^c)
=10^(-2) * (10^c)
Comparing powers of 10 on both sides,
a+b = c-2
This gives
c=a+b+2

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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okHedwig

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16 Dec 2025, 09:36

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IMO B

3.7* 5.8 = 21.46
hence eq becomes:
21.46* 10^(a+b)=0.2146 *10^c
eq powers of 10:
a+b-2= c-4
so, C= a+b+2

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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3.7 * (10^a)*5.8*(10^b) = 0.2146 * (10^c)

21.46 * 10^(a+b) = 0.2146 * 10^c

21.46 * 10^(a+b) = 21.46 * 10^(c+2)

Eliminate 21.46 from both side, since base is 10 and equal for both sides, we can directly compare the powers

a+b = c+2
c= a+b-2 A answer

VT10

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16 Dec 2025, 09:44

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(3.7*10^a) * (5.8*10^b) = 0.2146 * 10^c

= 21.46 * 10^a+b
Dividing whole by 10^2
= 0.2146 * 10^a+b-2
= 0.2146 * 10^c

So, c= a+b-2

So, Option A.

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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aka007

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16 Dec 2025, 09:48

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(3.7 x 10^a) x (5.8 x 10^b)= 0.2146 x 10^c
21.46 x 10 ^a+b= 0.2146 x 10^c
to compare LHS and RHS the base must be in same form. hence 0.2146 being converted to 21.46 x 10^-2

21.46 x 10^a+b= 21.46 x 10^c-2
a+b= c-2
c= a+b+2

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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Abhishake04

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16 Dec 2025, 09:50

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We have, (3.7*10_power_a)*(5.8_power_b)=0.2146*10_power_c
on multiplying, 21.46*10_power_(a+b)= (21.46*10_power_c)*(10_power_[-2]) ...
a+b=c-2
c=a+b+2

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16 Dec 2025, 09:50

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Here is the catch first if we multiply left side 3.7*5.8=21.46 then 10^a*10^b=10^(a+b)

So 21.46*10^(a+b)=21.46*10^(-2)*10^(c)

Follows 10^(a+b)=10^(c-2) bases are the same we can just make powers equal

Finally a+b=c-2 => c=a+b+2

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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Sumimasen

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16 Dec 2025, 09:51

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Rules of exponents
a^m * a^n = a^(m+n)....(eq. 1)

To solve this question, we need to group the numbers & powers of 10 both side and try to make coefficients at RHS & LHS equal.
(3.7 * 5.8) * (10^a * 10^b) = (0.2146) * 10^c
21.46 * 10^(a+b) = (0.2146) * 10^c (Apply eq.1)
0.2146 * 10^(2) * 10^(a+b) = 0.2146 * 10^c
0.2146 * 10^(a+b+2) = 0.2146 * 10^c

Now coefficients are equal, so equate powers of 10

a+b+2 = c (ANS B)

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16 Dec 2025, 09:53

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3.7 *10^a* 5.8*10^b = 21.46 * 10^(a+b) ==> 0.2146 * 10^c

i.e. to equate LHS with RHS, 21.46 can be written as 0.2146 * 10^2 and so you end up with 10^(a+b+2) = 10^c, i.e. a+b+2 = c

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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Hrudaya123

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16 Dec 2025, 09:57

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(3.7 * 10^a ) * (5.8 * 10^b) = 0.2146 * 10^c

lets simplify the left side of the equation
3.7 * 5.8 * 10^a + 10^b
21.46 * 10^ a+b ( when multiplying the power of 10 add the exponents )

which gives us
21.46 * 10^a +b = 0.2146* 10^c

now to write 21.46 as 0.2146 multiply it by 100 or 10^2 which gives us

21.46 = 0.2146 x 10^2

substitute it back in the equation

(0.2146 x 10^2) x 10^a+b = 0.2146 x 10^c

0.2146 x 10^a+b+2 = 0.2146 x 10^c

now if both the side are equal then the exponents must be equal

10^a+b+2 = 10^c

so the ans is B. a+b+2

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16 Dec 2025, 10:04

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Upon simplifying the equation given,
We get
$21.46 * 10^(a+b) = 0.2146 * 10^c$
Which then simplifies to
$0.2146 * 10^(a+b+2) = 0.2146 * 10^c$

So, c = a + b + 2, option B.

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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eeshajain

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16 Dec 2025, 10:04

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(3.7x10^a)(5.8x10^b)=0.2146x10^c
(37x10^a-1)(58x10^b-1)=2146x10^c-4
since, 37x58=2146,
(10^a)(10^b)=10^c-2
as the base is same,
a+b=c-2,
Hence,
c=a+b+2

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Just open the brackets:
We get LHS = 3.7 * 5.8 * 10^(a+b)
RHS = 0.2146 * 10^c

When you multiply 3.7*5.8 you get 21.46
So => 21.46 *10^(a+b) = 0.2146 * 10^(c)
We an also say
=> 21.46*10^(a+b) = 21.46*10^(c-2)

So from both ides we can say => a+b = c - 2 Hence C = a + b +2
Ans is B

Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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Ans: Option B
LHS: 3.7*10^a * 5.8*10^b = 21.46*10^(a+b) = 2146*10^(a+b+-2)
RHS: 0.2146*10^c = 2146*10^(c-4)
As LHS = RHS, we have
2146*10^(a+b-2) = 2146*10^(c-4)
10^(a+b-2) = 10^(c-2)
a+b-2 = c-4
a+b+2 = c
Option B.

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Bunuel

If $(3.7 * 10^a) * (5.8 * 10^b) = 0.2146 * 10^c$, what is c in terms of a and b?

A. a + b - 2
B. a + b + 2
C. (a + b)/2
D. ab - 2
E. ab + 2

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(3.7*10^a)(5.8*10^b)
3.7*5.8=21.46
10^a*10^b=10^a+b
21.46*10^a+b = 0.2146*10^c
Rewrite 21.46 as 0.2146*10^2
0.2146*10^2*10^a+b=0.2146*10^c
10^a+b+2=10^c
c=a+b+2
Hence, OPTION B.

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16 Dec 2025, 10:14

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Given the LHS, we can rewrite the same as 21.46* 10^(a+b)

We also know that 21.46= 0.2146*10^2

Therefore, 0.2146*10^2*10^(a+b) = 0.2146*10^c as per the questions

We can equate the power of 10 and get c = 2+a+b

Therefore, Option B

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16 Dec 2025, 10:19

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just mulitplying 3.7 with 5.8 gives use 21.46 a nice mirror to the 0.2146 on the other side.

therefore we can see make an equation as follows:

21.46*10^(a+b) = 0.2146*10^c
=> 0.2146*10^(-2)*10(a+b) = 0.2146*10^c
=> 0.2146*10^(a+b-2) = 0.2146*10^c
=> a+b-2 = c